Daily Papers

We are witnessing rapid progress in automatically generating and manipulating 3D assets due to the availability of pretrained text-image diffusion models. However, time-consuming optimization procedures are required for synthesizing each sample, hindering their potential for democratizing 3D content creation. Conversely, 3D diffusion models now train on million-scale 3D datasets, yielding high-quality text-conditional 3D samples within seconds. In this work, we present Spice-E - a neural network that adds structural guidance to 3D diffusion models, extending their usage beyond text-conditional generation. At its core, our framework introduces a cross-entity attention mechanism that allows for multiple entities (in particular, paired input and guidance 3D shapes) to interact via their internal representations within the denoising network. We utilize this mechanism for learning task-specific structural priors in 3D diffusion models from auxiliary guidance shapes. We show that our approach supports a variety of applications, including 3D stylization, semantic shape editing and text-conditional abstraction-to-3D, which transforms primitive-based abstractions into highly-expressive shapes. Extensive experiments demonstrate that Spice-E achieves SOTA performance over these tasks while often being considerably faster than alternative methods. Importantly, this is accomplished without tailoring our approach for any specific task.

Knowledge graph-based retrieval-augmented generation seeks to mitigate hallucinations in Large Language Models (LLMs) caused by insufficient or outdated knowledge. However, existing methods often fail to fully exploit the prior knowledge embedded in knowledge graphs (KGs), particularly their structural information and explicit or implicit constraints. The former can enhance the faithfulness of LLMs' reasoning, while the latter can improve the reliability of response generation. Motivated by these, we propose a trustworthy reasoning framework, termed Deliberation over Priors (DP), which sufficiently utilizes the priors contained in KGs. Specifically, DP adopts a progressive knowledge distillation strategy that integrates structural priors into LLMs through a combination of supervised fine-tuning and Kahneman-Tversky optimization, thereby improving the faithfulness of relation path generation. Furthermore, our framework employs a reasoning-introspection strategy, which guides LLMs to perform refined reasoning verification based on extracted constraint priors, ensuring the reliability of response generation. Extensive experiments on three benchmark datasets demonstrate that DP achieves new state-of-the-art performance, especially a Hit@1 improvement of 13% on the ComplexWebQuestions dataset, and generates highly trustworthy responses. We also conduct various analyses to verify its flexibility and practicality. The code is available at https://github.com/reml-group/Deliberation-on-Priors.

Reconstructing 3D objects from a single image guided by pretrained diffusion models has demonstrated promising outcomes. However, due to utilizing the case-agnostic rigid strategy, their generalization ability to arbitrary cases and the 3D consistency of reconstruction are still poor. In this work, we propose Consistent123, a case-aware two-stage method for highly consistent 3D asset reconstruction from one image with both 2D and 3D diffusion priors. In the first stage, Consistent123 utilizes only 3D structural priors for sufficient geometry exploitation, with a CLIP-based case-aware adaptive detection mechanism embedded within this process. In the second stage, 2D texture priors are introduced and progressively take on a dominant guiding role, delicately sculpting the details of the 3D model. Consistent123 aligns more closely with the evolving trends in guidance requirements, adaptively providing adequate 3D geometric initialization and suitable 2D texture refinement for different objects. Consistent123 can obtain highly 3D-consistent reconstruction and exhibits strong generalization ability across various objects. Qualitative and quantitative experiments show that our method significantly outperforms state-of-the-art image-to-3D methods. See https://Consistent123.github.io for a more comprehensive exploration of our generated 3D assets.

Current popular backbones in computer vision, such as Vision Transformers (ViT) and ResNets are trained to perceive the world from 2D images. However, to more effectively understand 3D structural priors in 2D backbones, we propose Mask3D to leverage existing large-scale RGB-D data in a self-supervised pre-training to embed these 3D priors into 2D learned feature representations. In contrast to traditional 3D contrastive learning paradigms requiring 3D reconstructions or multi-view correspondences, our approach is simple: we formulate a pre-text reconstruction task by masking RGB and depth patches in individual RGB-D frames. We demonstrate the Mask3D is particularly effective in embedding 3D priors into the powerful 2D ViT backbone, enabling improved representation learning for various scene understanding tasks, such as semantic segmentation, instance segmentation and object detection. Experiments show that Mask3D notably outperforms existing self-supervised 3D pre-training approaches on ScanNet, NYUv2, and Cityscapes image understanding tasks, with an improvement of +6.5% mIoU against the state-of-the-art Pri3D on ScanNet image semantic segmentation.

Category-Agnostic Pose Estimation (CAPE) localizes keypoints across diverse object categories with a single model, using one or a few annotated support images. Recent works have shown that using a pose graph (i.e., treating keypoints as nodes in a graph rather than isolated points) helps handle occlusions and break symmetry. However, these methods assume a static pose graph with equal-weight edges, leading to suboptimal results. We introduce EdgeCape, a novel framework that overcomes these limitations by predicting the graph's edge weights which optimizes localization. To further leverage structural priors, we propose integrating Markovian Structural Bias, which modulates the self-attention interaction between nodes based on the number of hops between them. We show that this improves the model's ability to capture global spatial dependencies. Evaluated on the MP-100 benchmark, which includes 100 categories and over 20K images, EdgeCape achieves state-of-the-art results in the 1-shot setting and leads among similar-sized methods in the 5-shot setting, significantly improving keypoint localization accuracy. Our code is publicly available.

Completing a corrupted image with correct structures and reasonable textures for a mixed scene remains an elusive challenge. Since the missing hole in a mixed scene of a corrupted image often contains various semantic information, conventional two-stage approaches utilizing structural information often lead to the problem of unreliable structural prediction and ambiguous image texture generation. In this paper, we propose a Semantic Guidance and Evaluation Network (SGE-Net) to iteratively update the structural priors and the inpainted image in an interplay framework of semantics extraction and image inpainting. It utilizes semantic segmentation map as guidance in each scale of inpainting, under which location-dependent inferences are re-evaluated, and, accordingly, poorly-inferred regions are refined in subsequent scales. Extensive experiments on real-world images of mixed scenes demonstrated the superiority of our proposed method over state-of-the-art approaches, in terms of clear boundaries and photo-realistic textures.

Leveraging visual priors from pre-trained text-to-image (T2I) generative models has shown success in dense prediction. However, dense prediction is inherently an image-to-image task, suggesting that image editing models, rather than T2I generative models, may be a more suitable foundation for fine-tuning. Motivated by this, we conduct a systematic analysis of the fine-tuning behaviors of both editors and generators for dense geometry estimation. Our findings show that editing models possess inherent structural priors, which enable them to converge more stably by ``refining" their innate features, and ultimately achieve higher performance than their generative counterparts. Based on these findings, we introduce FE2E, a framework that pioneeringly adapts an advanced editing model based on Diffusion Transformer (DiT) architecture for dense geometry prediction. Specifically, to tailor the editor for this deterministic task, we reformulate the editor's original flow matching loss into the ``consistent velocity" training objective. And we use logarithmic quantization to resolve the precision conflict between the editor's native BFloat16 format and the high precision demand of our tasks. Additionally, we leverage the DiT's global attention for a cost-free joint estimation of depth and normals in a single forward pass, enabling their supervisory signals to mutually enhance each other. Without scaling up the training data, FE2E achieves impressive performance improvements in zero-shot monocular depth and normal estimation across multiple datasets. Notably, it achieves over 35\% performance gains on the ETH3D dataset and outperforms the DepthAnything series, which is trained on 100times data. The project page can be accessed https://amap-ml.github.io/FE2E/{here}.

Nearly all real world tasks are inherently partially observable, necessitating the use of memory in Reinforcement Learning (RL). Most model-free approaches summarize the trajectory into a latent Markov state using memory models borrowed from Supervised Learning (SL), even though RL tends to exhibit different training and efficiency characteristics. Addressing this discrepancy, we introduce Fast and Forgetful Memory, an algorithm-agnostic memory model designed specifically for RL. Our approach constrains the model search space via strong structural priors inspired by computational psychology. It is a drop-in replacement for recurrent neural networks (RNNs) in recurrent RL algorithms, achieving greater reward than RNNs across various recurrent benchmarks and algorithms without changing any hyperparameters. Moreover, Fast and Forgetful Memory exhibits training speeds two orders of magnitude faster than RNNs, attributed to its logarithmic time and linear space complexity. Our implementation is available at https://github.com/proroklab/ffm.

As there are now millions of publicly available neural networks, searching and analyzing large model repositories becomes increasingly important. Navigating so many models requires an atlas, but as most models are poorly documented charting such an atlas is challenging. To explore the hidden potential of model repositories, we chart a preliminary atlas representing the documented fraction of Hugging Face. It provides stunning visualizations of the model landscape and evolution. We demonstrate several applications of this atlas including predicting model attributes (e.g., accuracy), and analyzing trends in computer vision models. However, as the current atlas remains incomplete, we propose a method for charting undocumented regions. Specifically, we identify high-confidence structural priors based on dominant real-world model training practices. Leveraging these priors, our approach enables accurate mapping of previously undocumented areas of the atlas. We publicly release our datasets, code, and interactive atlas.

Satellite image time-series analysis demands fine-grained spatial-temporal reasoning, which remains a challenge for existing multimodal large language models (MLLMs). In this work, we study the capabilities of MLLMs on a novel task that jointly targets temporal change understanding and future scene generation, aiming to assess their potential for modeling complex multimodal dynamics over time. We propose TAMMs, a Temporal-Aware Multimodal Model for satellite image change understanding and forecasting, which enhances frozen MLLMs with lightweight temporal modules for structured sequence encoding and contextual prompting. To guide future image generation, TAMMs introduces a Semantic-Fused Control Injection (SFCI) mechanism that adaptively combines high-level semantic reasoning and structural priors within an enhanced ControlNet. This dual-path conditioning enables temporally consistent and semantically grounded image synthesis. Experiments demonstrate that TAMMs outperforms strong MLLM baselines in both temporal change understanding and future image forecasting tasks, highlighting how carefully designed temporal reasoning and semantic fusion can unlock the full potential of MLLMs for spatio-temporal understanding.

Large Language Models (LLMs) have been shown to be effective models of the human language system, with some models predicting most explainable variance of brain activity in current datasets. Even in untrained models, the representations induced by architectural priors can exhibit reasonable alignment to brain data. In this work, we investigate the key architectural components driving the surprising alignment of untrained models. To estimate LLM-to-brain similarity, we first select language-selective units within an LLM, similar to how neuroscientists identify the language network in the human brain. We then benchmark the brain alignment of these LLM units across five different brain recording datasets. By isolating critical components of the Transformer architecture, we identify tokenization strategy and multihead attention as the two major components driving brain alignment. A simple form of recurrence further improves alignment. We further demonstrate this quantitative brain alignment of our model by reproducing landmark studies in the language neuroscience field, showing that localized model units -- just like language voxels measured empirically in the human brain -- discriminate more reliably between lexical than syntactic differences, and exhibit similar response profiles under the same experimental conditions. Finally, we demonstrate the utility of our model's representations for language modeling, achieving improved sample and parameter efficiency over comparable architectures. Our model's estimates of surprisal sets a new state-of-the-art in the behavioral alignment to human reading times. Taken together, we propose a highly brain- and behaviorally-aligned model that conceptualizes the human language system as an untrained shallow feature encoder, with structural priors, combined with a trained decoder to achieve efficient and performant language processing.

Four-dimensional cone-beam computed tomography (4D CBCT) provides respiration-resolved images and can be used for image-guided radiation therapy. However, the ability to reveal respiratory motion comes at the cost of image artifacts. As raw projection data are sorted into multiple respiratory phases, the cone-beam projections become much sparser and the reconstructed 4D CBCT images will be covered by severe streak artifacts. Although several deep learning-based methods have been proposed to address this issue, most algorithms employ 2D network models as backbones, neglecting the intrinsic structural priors within 4D CBCT images. In this paper, we first explore the origin and appearance of streak artifacts in 4D CBCT images. We find that streak artifacts exhibit a unique rotational motion along with the patient's respiration, distinguishable from diaphragm-driven respiratory motion in the spatiotemporal domain. Therefore, we propose a novel 4D neural network model, RSTAR4D-Net, designed to address Rotational STreak Artifact Reduction by integrating the spatial and temporal information within 4D CBCT images. Specifically, we overcome the computational and training difficulties of a 4D neural network. The specially designed model adopts an efficient implementation of 4D convolutions to reduce computational costs and thus can process the whole 4D image in one pass. Additionally, a Tetris training strategy pertinent to the separable 4D convolutions is proposed to effectively train the model using limited 4D training samples. Extensive experiments substantiate the effectiveness of our proposed method, and the RSTAR4D-Net shows superior performance compared to other methods. The source code and dynamic demos are available at https://github.com/ivy9092111111/RSTAR.

Graphs can be leveraged to model polyphonic multitrack symbolic music, where notes, chords and entire sections may be linked at different levels of the musical hierarchy by tonal and rhythmic relationships. Nonetheless, there is a lack of works that consider graph representations in the context of deep learning systems for music generation. This paper bridges this gap by introducing a novel graph representation for music and a deep Variational Autoencoder that generates the structure and the content of musical graphs separately, one after the other, with a hierarchical architecture that matches the structural priors of music. By separating the structure and content of musical graphs, it is possible to condition generation by specifying which instruments are played at certain times. This opens the door to a new form of human-computer interaction in the context of music co-creation. After training the model on existing MIDI datasets, the experiments show that the model is able to generate appealing short and long musical sequences and to realistically interpolate between them, producing music that is tonally and rhythmically consistent. Finally, the visualization of the embeddings shows that the model is able to organize its latent space in accordance with known musical concepts.

Human perception of 3D shapes goes beyond reconstructing them as a set of points or a composition of geometric primitives: we also effortlessly understand higher-level shape structure such as the repetition and reflective symmetry of object parts. In contrast, recent advances in 3D shape sensing focus more on low-level geometry but less on these higher-level relationships. In this paper, we propose 3D shape programs, integrating bottom-up recognition systems with top-down, symbolic program structure to capture both low-level geometry and high-level structural priors for 3D shapes. Because there are no annotations of shape programs for real shapes, we develop neural modules that not only learn to infer 3D shape programs from raw, unannotated shapes, but also to execute these programs for shape reconstruction. After initial bootstrapping, our end-to-end differentiable model learns 3D shape programs by reconstructing shapes in a self-supervised manner. Experiments demonstrate that our model accurately infers and executes 3D shape programs for highly complex shapes from various categories. It can also be integrated with an image-to-shape module to infer 3D shape programs directly from an RGB image, leading to 3D shape reconstructions that are both more accurate and more physically plausible.

Blind face restoration from low-quality (LQ) images is a challenging task that requires not only high-fidelity image reconstruction but also the preservation of facial identity. While diffusion models like Stable Diffusion have shown promise in generating high-quality (HQ) images, their VAE modules are typically trained only on HQ data, resulting in semantic misalignment when encoding LQ inputs. This mismatch significantly weakens the effectiveness of LQ conditions during the denoising process. Existing approaches often tackle this issue by retraining the VAE encoder, which is computationally expensive and memory-intensive. To address this limitation efficiently, we propose LAFR (Latent Alignment for Face Restoration), a novel codebook-based latent space adapter that aligns the latent distribution of LQ images with that of HQ counterparts, enabling semantically consistent diffusion sampling without altering the original VAE. To further enhance identity preservation, we introduce a multi-level restoration loss that combines constraints from identity embeddings and facial structural priors. Additionally, by leveraging the inherent structural regularity of facial images, we show that lightweight finetuning of diffusion prior on just 0.9% of FFHQ dataset is sufficient to achieve results comparable to state-of-the-art methods, reduce training time by 70%. Extensive experiments on both synthetic and real-world face restoration benchmarks demonstrate the effectiveness and efficiency of LAFR, achieving high-quality, identity-preserving face reconstruction from severely degraded inputs.

Self-occlusion is common when capturing people in the wild, where the performer do not follow predefined motion scripts. This challenges existing monocular human reconstruction systems that assume full body visibility. We introduce Self-Occluded Avatar Recovery (SOAR), a method for complete human reconstruction from partial observations where parts of the body are entirely unobserved. SOAR leverages structural normal prior and generative diffusion prior to address such an ill-posed reconstruction problem. For structural normal prior, we model human with an reposable surfel model with well-defined and easily readable shapes. For generative diffusion prior, we perform an initial reconstruction and refine it using score distillation. On various benchmarks, we show that SOAR performs favorably than state-of-the-art reconstruction and generation methods, and on-par comparing to concurrent works. Additional video results and code are available at https://soar-avatar.github.io/.

3D affordance reasoning is essential in associating human instructions with the functional regions of 3D objects, facilitating precise, task-oriented manipulations in embodied AI. However, current methods, which predominantly depend on sparse 3D point clouds, exhibit limited generalizability and robustness due to their sensitivity to coordinate variations and the inherent sparsity of the data. By contrast, 3D Gaussian Splatting (3DGS) delivers high-fidelity, real-time rendering with minimal computational overhead by representing scenes as dense, continuous distributions. This positions 3DGS as a highly effective approach for capturing fine-grained affordance details and improving recognition accuracy. Nevertheless, its full potential remains largely untapped due to the absence of large-scale, 3DGS-specific affordance datasets. To overcome these limitations, we present 3DAffordSplat, the first large-scale, multi-modal dataset tailored for 3DGS-based affordance reasoning. This dataset includes 23,677 Gaussian instances, 8,354 point cloud instances, and 6,631 manually annotated affordance labels, encompassing 21 object categories and 18 affordance types. Building upon this dataset, we introduce AffordSplatNet, a novel model specifically designed for affordance reasoning using 3DGS representations. AffordSplatNet features an innovative cross-modal structure alignment module that exploits structural consistency priors to align 3D point cloud and 3DGS representations, resulting in enhanced affordance recognition accuracy. Extensive experiments demonstrate that the 3DAffordSplat dataset significantly advances affordance learning within the 3DGS domain, while AffordSplatNet consistently outperforms existing methods across both seen and unseen settings, highlighting its robust generalization capabilities.

Arbitrary-scale video super-resolution (AVSR) aims to enhance the resolution of video frames, potentially at various scaling factors, which presents several challenges regarding spatial detail reproduction, temporal consistency, and computational complexity. In this paper, we first describe a strong baseline for AVSR by putting together three variants of elementary building blocks: 1) a flow-guided recurrent unit that aggregates spatiotemporal information from previous frames, 2) a flow-refined cross-attention unit that selects spatiotemporal information from future frames, and 3) a hyper-upsampling unit that generates scaleaware and content-independent upsampling kernels. We then introduce ST-AVSR by equipping our baseline with a multi-scale structural and textural prior computed from the pre-trained VGG network. This prior has proven effective in discriminating structure and texture across different locations and scales, which is beneficial for AVSR. Comprehensive experiments show that ST-AVSR significantly improves super-resolution quality, generalization ability, and inference speed over the state-of-theart. The code is available at https://github.com/shangwei5/ST-AVSR.

We introduce ShowRoom3D, a three-stage approach for generating high-quality 3D room-scale scenes from texts. Previous methods using 2D diffusion priors to optimize neural radiance fields for generating room-scale scenes have shown unsatisfactory quality. This is primarily attributed to the limitations of 2D priors lacking 3D awareness and constraints in the training methodology. In this paper, we utilize a 3D diffusion prior, MVDiffusion, to optimize the 3D room-scale scene. Our contributions are in two aspects. Firstly, we propose a progressive view selection process to optimize NeRF. This involves dividing the training process into three stages, gradually expanding the camera sampling scope. Secondly, we propose the pose transformation method in the second stage. It will ensure MVDiffusion provide the accurate view guidance. As a result, ShowRoom3D enables the generation of rooms with improved structural integrity, enhanced clarity from any view, reduced content repetition, and higher consistency across different perspectives. Extensive experiments demonstrate that our method, significantly outperforms state-of-the-art approaches by a large margin in terms of user study.

3D Gaussian Splatting (3DGS) excels in photorealistic scene reconstruction but struggles with stylized scenarios (e.g., cartoons, games) due to fragmented textures, semantic misalignment, and limited adaptability to abstract aesthetics. We propose StyleMe3D, a holistic framework for 3D GS style transfer that integrates multi-modal style conditioning, multi-level semantic alignment, and perceptual quality enhancement. Our key insights include: (1) optimizing only RGB attributes preserves geometric integrity during stylization; (2) disentangling low-, medium-, and high-level semantics is critical for coherent style transfer; (3) scalability across isolated objects and complex scenes is essential for practical deployment. StyleMe3D introduces four novel components: Dynamic Style Score Distillation (DSSD), leveraging Stable Diffusion's latent space for semantic alignment; Contrastive Style Descriptor (CSD) for localized, content-aware texture transfer; Simultaneously Optimized Scale (SOS) to decouple style details and structural coherence; and 3D Gaussian Quality Assessment (3DG-QA), a differentiable aesthetic prior trained on human-rated data to suppress artifacts and enhance visual harmony. Evaluated on NeRF synthetic dataset (objects) and tandt db (scenes) datasets, StyleMe3D outperforms state-of-the-art methods in preserving geometric details (e.g., carvings on sculptures) and ensuring stylistic consistency across scenes (e.g., coherent lighting in landscapes), while maintaining real-time rendering. This work bridges photorealistic 3D GS and artistic stylization, unlocking applications in gaming, virtual worlds, and digital art.

Diffusion models have emerged as the dominant paradigm for style transfer, but their text-driven mechanism is hindered by a core limitation: it treats textual descriptions as uniform, monolithic guidance. This limitation overlooks the semantic gap between the non-spatial nature of textual descriptions and the spatially-aware attributes of visual style, often leading to the loss of semantic structure and fine-grained details during stylization. In this paper, we propose StyDeco, an unsupervised framework that resolves this limitation by learning text representations specifically tailored for the style transfer task. Our framework first employs Prior-Guided Data Distillation (PGD), a strategy designed to distill stylistic knowledge without human supervision. It leverages a powerful frozen generative model to automatically synthesize pseudo-paired data. Subsequently, we introduce Contrastive Semantic Decoupling (CSD), a task-specific objective that adapts a text encoder using domain-specific weights. CSD performs a two-class clustering in the semantic space, encouraging source and target representations to form distinct clusters. Extensive experiments on three classic benchmarks demonstrate that our framework outperforms several existing approaches in both stylistic fidelity and structural preservation, highlighting its effectiveness in style transfer with semantic preservation. In addition, our framework supports a unique de-stylization process, further demonstrating its extensibility. Our code is vailable at https://github.com/QuanjianSong/StyDeco.

We introduce PortraitGen, a powerful portrait video editing method that achieves consistent and expressive stylization with multimodal prompts. Traditional portrait video editing methods often struggle with 3D and temporal consistency, and typically lack in rendering quality and efficiency. To address these issues, we lift the portrait video frames to a unified dynamic 3D Gaussian field, which ensures structural and temporal coherence across frames. Furthermore, we design a novel Neural Gaussian Texture mechanism that not only enables sophisticated style editing but also achieves rendering speed over 100FPS. Our approach incorporates multimodal inputs through knowledge distilled from large-scale 2D generative models. Our system also incorporates expression similarity guidance and a face-aware portrait editing module, effectively mitigating degradation issues associated with iterative dataset updates. Extensive experiments demonstrate the temporal consistency, editing efficiency, and superior rendering quality of our method. The broad applicability of the proposed approach is demonstrated through various applications, including text-driven editing, image-driven editing, and relighting, highlighting its great potential to advance the field of video editing. Demo videos and released code are provided in our project page: https://ustc3dv.github.io/PortraitGen/

Scalable Vector Graphics (SVGs) are highly favored by designers due to their resolution independence and well-organized layer structure. Although existing text-to-vector (T2V) generation methods can create SVGs from text prompts, they often overlook an important need in practical applications: style customization, which is vital for producing a collection of vector graphics with consistent visual appearance and coherent aesthetics. Extending existing T2V methods for style customization poses certain challenges. Optimization-based T2V models can utilize the priors of text-to-image (T2I) models for customization, but struggle with maintaining structural regularity. On the other hand, feed-forward T2V models can ensure structural regularity, yet they encounter difficulties in disentangling content and style due to limited SVG training data. To address these challenges, we propose a novel two-stage style customization pipeline for SVG generation, making use of the advantages of both feed-forward T2V models and T2I image priors. In the first stage, we train a T2V diffusion model with a path-level representation to ensure the structural regularity of SVGs while preserving diverse expressive capabilities. In the second stage, we customize the T2V diffusion model to different styles by distilling customized T2I models. By integrating these techniques, our pipeline can generate high-quality and diverse SVGs in custom styles based on text prompts in an efficient feed-forward manner. The effectiveness of our method has been validated through extensive experiments. The project page is https://customsvg.github.io.

We introduce nested diffusion models, an efficient and powerful hierarchical generative framework that substantially enhances the generation quality of diffusion models, particularly for images of complex scenes. Our approach employs a series of diffusion models to progressively generate latent variables at different semantic levels. Each model in this series is conditioned on the output of the preceding higher-level models, culminating in image generation. Hierarchical latent variables guide the generation process along predefined semantic pathways, allowing our approach to capture intricate structural details while significantly improving image quality. To construct these latent variables, we leverage a pre-trained visual encoder, which learns strong semantic visual representations, and modulate its capacity via dimensionality reduction and noise injection. Across multiple datasets, our system demonstrates significant enhancements in image quality for both unconditional and class/text conditional generation. Moreover, our unconditional generation system substantially outperforms the baseline conditional system. These advancements incur minimal computational overhead as the more abstract levels of our hierarchy work with lower-dimensional representations.

High-fidelity head avatar reconstruction plays a crucial role in AR/VR, gaming, and multimedia content creation. Recent advances in 3D Gaussian Splatting (3DGS) have demonstrated effectiveness in modeling complex geometry with real-time rendering capability and are now widely used in high-fidelity head avatar reconstruction tasks. However, existing 3DGS-based methods still face significant challenges in capturing fine-grained facial expressions and preserving local texture continuity, especially in highly deformable regions. To mitigate these limitations, we propose a novel 3DGS-based framework termed EAvatar for head reconstruction that is both expression-aware and deformation-aware. Our method introduces a sparse expression control mechanism, where a small number of key Gaussians are used to influence the deformation of their neighboring Gaussians, enabling accurate modeling of local deformations and fine-scale texture transitions. Furthermore, we leverage high-quality 3D priors from pretrained generative models to provide a more reliable facial geometry, offering structural guidance that improves convergence stability and shape accuracy during training. Experimental results demonstrate that our method produces more accurate and visually coherent head reconstructions with improved expression controllability and detail fidelity.

We propose HYBRIDDEPTH, a robust depth estimation pipeline that addresses the unique challenges of depth estimation for mobile AR, such as scale ambiguity, hardware heterogeneity, and generalizability. HYBRIDDEPTH leverages the camera features available on mobile devices. It effectively combines the scale accuracy inherent in Depth from Focus (DFF) methods with the generalization capabilities enabled by strong single-image depth priors. By utilizing the focal planes of a mobile camera, our approach accurately captures depth values from focused pixels and applies these values to compute scale and shift parameters for transforming relative depths into metric depths. We test our pipeline as an end-to-end system, with a newly developed mobile client to capture focal stacks, which are then sent to a GPU-powered server for depth estimation. Through comprehensive quantitative and qualitative analyses, we demonstrate that HYBRIDDEPTH not only outperforms state-of-the-art (SOTA) models in common datasets (DDFF12, NYU Depth v2) and a real-world AR dataset ARKitScenes but also demonstrates strong zero-shot generalization. For example, HYBRIDDEPTH trained on NYU Depth v2 achieves comparable performance on the DDFF12 to existing models trained on DDFF12. it also outperforms all the SOTA models in zero-shot performance on the ARKitScenes dataset. Additionally, we conduct a qualitative comparison between our model and the ARCore framework, demonstrating that our models output depth maps are significantly more accurate in terms of structural details and metric accuracy. The source code of this project is available at github.

Recently, generalizable feed-forward methods based on 3D Gaussian Splatting have gained significant attention for their potential to reconstruct 3D scenes using finite resources. These approaches create a 3D radiance field, parameterized by per-pixel 3D Gaussian primitives, from just a few images in a single forward pass. However, unlike multi-view methods that benefit from cross-view correspondences, 3D scene reconstruction with a single-view image remains an underexplored area. In this work, we introduce CATSplat, a novel generalizable transformer-based framework designed to break through the inherent constraints in monocular settings. First, we propose leveraging textual guidance from a visual-language model to complement insufficient information from a single image. By incorporating scene-specific contextual details from text embeddings through cross-attention, we pave the way for context-aware 3D scene reconstruction beyond relying solely on visual cues. Moreover, we advocate utilizing spatial guidance from 3D point features toward comprehensive geometric understanding under single-view settings. With 3D priors, image features can capture rich structural insights for predicting 3D Gaussians without multi-view techniques. Extensive experiments on large-scale datasets demonstrate the state-of-the-art performance of CATSplat in single-view 3D scene reconstruction with high-quality novel view synthesis.

3D Gaussian Splatting (3D-GS) has recently attracted great attention with real-time and photo-realistic renderings. This technique typically takes perspective images as input and optimizes a set of 3D elliptical Gaussians by splatting them onto the image planes, resulting in 2D Gaussians. However, applying 3D-GS to panoramic inputs presents challenges in effectively modeling the projection onto the spherical surface of {360^circ} images using 2D Gaussians. In practical applications, input panoramas are often sparse, leading to unreliable initialization of 3D Gaussians and subsequent degradation of 3D-GS quality. In addition, due to the under-constrained geometry of texture-less planes (e.g., walls and floors), 3D-GS struggles to model these flat regions with elliptical Gaussians, resulting in significant floaters in novel views. To address these issues, we propose 360-GS, a novel 360^{circ} Gaussian splatting for a limited set of panoramic inputs. Instead of splatting 3D Gaussians directly onto the spherical surface, 360-GS projects them onto the tangent plane of the unit sphere and then maps them to the spherical projections. This adaptation enables the representation of the projection using Gaussians. We guide the optimization of 360-GS by exploiting layout priors within panoramas, which are simple to obtain and contain strong structural information about the indoor scene. Our experimental results demonstrate that 360-GS allows panoramic rendering and outperforms state-of-the-art methods with fewer artifacts in novel view synthesis, thus providing immersive roaming in indoor scenarios.

Generative models trained on extensive high-quality datasets effectively capture the structural and statistical properties of clean images, rendering them powerful priors for transforming degraded features into clean ones in image restoration. VAR, a novel image generative paradigm, surpasses diffusion models in generation quality by applying a next-scale prediction approach. It progressively captures both global structures and fine-grained details through the autoregressive process, consistent with the multi-scale restoration principle widely acknowledged in the restoration community. Furthermore, we observe that during the image reconstruction process utilizing VAR, scale predictions automatically modulate the input, facilitating the alignment of representations at subsequent scales with the distribution of clean images. To harness VAR's adaptive distribution alignment capability in image restoration tasks, we formulate the multi-scale latent representations within VAR as the restoration prior, thus advancing our delicately designed VarFormer framework. The strategic application of these priors enables our VarFormer to achieve remarkable generalization on unseen tasks while also reducing training computational costs. Extensive experiments underscores that our VarFormer outperforms existing multi-task image restoration methods across various restoration tasks.

Multimodal Large Language Models (MLLMs) have emerged as a central focus in both industry and academia, but often suffer from biases introduced by visual and language priors, which can lead to multimodal hallucination. These biases arise from the visual encoder and the Large Language Model (LLM) backbone, affecting the attention mechanism responsible for aligning multimodal inputs. Existing decoding-based mitigation methods focus on statistical correlations and overlook the causal relationships between attention mechanisms and model output, limiting their effectiveness in addressing these biases. To tackle this issue, we propose a causal inference framework termed CausalMM that applies structural causal modeling to MLLMs, treating modality priors as a confounder between attention mechanisms and output. Specifically, by employing backdoor adjustment and counterfactual reasoning at both the visual and language attention levels, our method mitigates the negative effects of modality priors and enhances the alignment of MLLM's inputs and outputs, with a maximum score improvement of 65.3% on 6 VLind-Bench indicators and 164 points on MME Benchmark compared to conventional methods. Extensive experiments validate the effectiveness of our approach while being a plug-and-play solution. Our code is available at: https://github.com/The-Martyr/CausalMM

Recently, extensive deep learning architectures and pretraining strategies have been explored to support downstream protein applications. Additionally, domain-specific models incorporating biological knowledge have been developed to enhance performance in specialized tasks. In this work, we introduce Protap, a comprehensive benchmark that systematically compares backbone architectures, pretraining strategies, and domain-specific models across diverse and realistic downstream protein applications. Specifically, Protap covers five applications: three general tasks and two novel specialized tasks, i.e., enzyme-catalyzed protein cleavage site prediction and targeted protein degradation, which are industrially relevant yet missing from existing benchmarks. For each application, Protap compares various domain-specific models and general architectures under multiple pretraining settings. Our empirical studies imply that: (i) Though large-scale pretraining encoders achieve great results, they often underperform supervised encoders trained on small downstream training sets. (ii) Incorporating structural information during downstream fine-tuning can match or even outperform protein language models pretrained on large-scale sequence corpora. (iii) Domain-specific biological priors can enhance performance on specialized downstream tasks. Code and datasets are publicly available at https://github.com/Trust-App-AI-Lab/protap.

Powerful priors allow us to perform inference with insufficient information. In this paper, we propose an autoregressive prior for 3D shapes to solve multimodal 3D tasks such as shape completion, reconstruction, and generation. We model the distribution over 3D shapes as a non-sequential autoregressive distribution over a discretized, low-dimensional, symbolic grid-like latent representation of 3D shapes. This enables us to represent distributions over 3D shapes conditioned on information from an arbitrary set of spatially anchored query locations and thus perform shape completion in such arbitrary settings (e.g., generating a complete chair given only a view of the back leg). We also show that the learned autoregressive prior can be leveraged for conditional tasks such as single-view reconstruction and language-based generation. This is achieved by learning task-specific naive conditionals which can be approximated by light-weight models trained on minimal paired data. We validate the effectiveness of the proposed method using both quantitative and qualitative evaluation and show that the proposed method outperforms the specialized state-of-the-art methods trained for individual tasks. The project page with code and video visualizations can be found at https://yccyenchicheng.github.io/AutoSDF/.

Structured variational autoencoders (SVAEs) combine probabilistic graphical model priors on latent variables, deep neural networks to link latent variables to observed data, and structure-exploiting algorithms for approximate posterior inference. These models are particularly appealing for sequential data, where the prior can capture temporal dependencies. However, despite their conceptual elegance, SVAEs have proven difficult to implement, and more general approaches have been favored in practice. Here, we revisit SVAEs using modern machine learning tools and demonstrate their advantages over more general alternatives in terms of both accuracy and efficiency. First, we develop a modern implementation for hardware acceleration, parallelization, and automatic differentiation of the message passing algorithms at the core of the SVAE. Second, we show that by exploiting structure in the prior, the SVAE learns more accurate models and posterior distributions, which translate into improved performance on prediction tasks. Third, we show how the SVAE can naturally handle missing data, and we leverage this ability to develop a novel, self-supervised training approach. Altogether, these results show that the time is ripe to revisit structured variational autoencoders.

Priors are essential for reconstructing images from noisy and/or incomplete measurements. The choice of the prior determines both the quality and uncertainty of recovered images. We propose turning score-based diffusion models into principled image priors ("score-based priors") for analyzing a posterior of images given measurements. Previously, probabilistic priors were limited to handcrafted regularizers and simple distributions. In this work, we empirically validate the theoretically-proven probability function of a score-based diffusion model. We show how to sample from resulting posteriors by using this probability function for variational inference. Our results, including experiments on denoising, deblurring, and interferometric imaging, suggest that score-based priors enable principled inference with a sophisticated, data-driven image prior.

The Bayesian treatment of neural networks dictates that a prior distribution is specified over their weight and bias parameters. This poses a challenge because modern neural networks are characterized by a large number of parameters, and the choice of these priors has an uncontrolled effect on the induced functional prior, which is the distribution of the functions obtained by sampling the parameters from their prior distribution. We argue that this is a hugely limiting aspect of Bayesian deep learning, and this work tackles this limitation in a practical and effective way. Our proposal is to reason in terms of functional priors, which are easier to elicit, and to "tune" the priors of neural network parameters in a way that they reflect such functional priors. Gaussian processes offer a rigorous framework to define prior distributions over functions, and we propose a novel and robust framework to match their prior with the functional prior of neural networks based on the minimization of their Wasserstein distance. We provide vast experimental evidence that coupling these priors with scalable Markov chain Monte Carlo sampling offers systematically large performance improvements over alternative choices of priors and state-of-the-art approximate Bayesian deep learning approaches. We consider this work a considerable step in the direction of making the long-standing challenge of carrying out a fully Bayesian treatment of neural networks, including convolutional neural networks, a concrete possibility.

Posterior sampling allows the exploitation of prior knowledge of the environment's transition dynamics to improve the sample efficiency of reinforcement learning. The prior is typically specified as a class of parametric distributions, a task that can be cumbersome in practice, often resulting in the choice of uninformative priors. In this work, we propose a novel posterior sampling approach in which the prior is given as a (partial) causal graph over the environment's variables. The latter is often more natural to design, such as listing known causal dependencies between biometric features in a medical treatment study. Specifically, we propose a hierarchical Bayesian procedure, called C-PSRL, simultaneously learning the full causal graph at the higher level and the parameters of the resulting factored dynamics at the lower level. For this procedure, we provide an analysis of its Bayesian regret, which explicitly connects the regret rate with the degree of prior knowledge. Our numerical evaluation conducted in illustrative domains confirms that C-PSRL strongly improves the efficiency of posterior sampling with an uninformative prior while performing close to posterior sampling with the full causal graph.

We present TabPFN, a trained Transformer that can do supervised classification for small tabular datasets in less than a second, needs no hyperparameter tuning and is competitive with state-of-the-art classification methods. TabPFN performs in-context learning (ICL), it learns to make predictions using sequences of labeled examples (x, f(x)) given in the input, without requiring further parameter updates. TabPFN is fully entailed in the weights of our network, which accepts training and test samples as a set-valued input and yields predictions for the entire test set in a single forward pass. TabPFN is a Prior-Data Fitted Network (PFN) and is trained offline once, to approximate Bayesian inference on synthetic datasets drawn from our prior. This prior incorporates ideas from causal reasoning: It entails a large space of structural causal models with a preference for simple structures. On the 18 datasets in the OpenML-CC18 suite that contain up to 1 000 training data points, up to 100 purely numerical features without missing values, and up to 10 classes, we show that our method clearly outperforms boosted trees and performs on par with complex state-of-the-art AutoML systems with up to 230times speedup. This increases to a 5 700times speedup when using a GPU. We also validate these results on an additional 67 small numerical datasets from OpenML. We provide all our code, the trained TabPFN, an interactive browser demo and a Colab notebook at https://github.com/automl/TabPFN.

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are often best described using continuous-time stochastic processes. Unfortunately, most existing structure learning approaches assume that the underlying process evolves in discrete-time and/or observations occur at regular time intervals. These mismatched assumptions can often lead to incorrect learned structures and models. In this work, we introduce a novel structure learning method, SCOTCH, which combines neural stochastic differential equations (SDE) with variational inference to infer a posterior distribution over possible structures. This continuous-time approach can naturally handle both learning from and predicting observations at arbitrary time points. Theoretically, we establish sufficient conditions for an SDE and SCOTCH to be structurally identifiable, and prove its consistency under infinite data limits. Empirically, we demonstrate that our approach leads to improved structure learning performance on both synthetic and real-world datasets compared to relevant baselines under regular and irregular sampling intervals.

Sequential Bayesian inference can be used for continual learning to prevent catastrophic forgetting of past tasks and provide an informative prior when learning new tasks. We revisit sequential Bayesian inference and test whether having access to the true posterior is guaranteed to prevent catastrophic forgetting in Bayesian neural networks. To do this we perform sequential Bayesian inference using Hamiltonian Monte Carlo. We propagate the posterior as a prior for new tasks by fitting a density estimator on Hamiltonian Monte Carlo samples. We find that this approach fails to prevent catastrophic forgetting demonstrating the difficulty in performing sequential Bayesian inference in neural networks. From there we study simple analytical examples of sequential Bayesian inference and CL and highlight the issue of model misspecification which can lead to sub-optimal continual learning performance despite exact inference. Furthermore, we discuss how task data imbalances can cause forgetting. From these limitations, we argue that we need probabilistic models of the continual learning generative process rather than relying on sequential Bayesian inference over Bayesian neural network weights. In this vein, we also propose a simple baseline called Prototypical Bayesian Continual Learning, which is competitive with state-of-the-art Bayesian continual learning methods on class incremental continual learning vision benchmarks.

A desired closure property in Bayesian probability is that an updated posterior distribution be in the same class of distributions --- say Gaussians --- as the prior distribution. When the updating takes place via a statistical model, one calls the class of prior distributions the `conjugate priors' of the model. This paper gives (1) an abstract formulation of this notion of conjugate prior, using channels, in a graphical language, (2) a simple abstract proof that such conjugate priors yield Bayesian inversions, and (3) a logical description of conjugate priors that highlights the required closure of the priors under updating. The theory is illustrated with several standard examples, also covering multiple updating.

Recent works have revealed that infinitely-wide feed-forward or recurrent neural networks of any architecture correspond to Gaussian processes referred to as Neural Network Gaussian Processes (NNGPs). While these works have extended the class of neural networks converging to Gaussian processes significantly, however, there has been little focus on broadening the class of stochastic processes that such neural networks converge to. In this work, inspired by the scale mixture of Gaussian random variables, we propose the scale mixture of NNGPs for which we introduce a prior distribution on the scale of the last-layer parameters. We show that simply introducing a scale prior on the last-layer parameters can turn infinitely-wide neural networks of any architecture into a richer class of stochastic processes. With certain scale priors, we obtain heavy-tailed stochastic processes, and in the case of inverse gamma priors, we recover Student's t processes. We further analyze the distributions of the neural networks initialized with our prior setting and trained with gradient descents and obtain similar results as for NNGPs. We present a practical posterior-inference algorithm for the scale mixture of NNGPs and empirically demonstrate its usefulness on regression and classification tasks. In particular, we show that in both tasks, the heavy-tailed stochastic processes obtained from our framework are robust to out-of-distribution data.

This paper presents a Bayesian nonparametric latent feature model specially suitable for exploratory analysis of high-dimensional count data. We perform a non-negative doubly sparse matrix factorization that has two main advantages: not only we are able to better approximate the row input distributions, but the inferred topics are also easier to interpret. By combining the three-parameter and restricted Indian buffet processes into a single prior, we increase the model flexibility, allowing for a full spectrum of sparse solutions in the latent space. We demonstrate the usefulness of our approach in the analysis of countries' economic structure. Compared to other approaches, empirical results show our model's ability to give easy-to-interpret information and better capture the underlying sparsity structure of data.

Currently, it is hard to reap the benefits of deep learning for Bayesian methods, which allow the explicit specification of prior knowledge and accurately capture model uncertainty. We present Prior-Data Fitted Networks (PFNs). PFNs leverage large-scale machine learning techniques to approximate a large set of posteriors. The only requirement for PFNs to work is the ability to sample from a prior distribution over supervised learning tasks (or functions). Our method restates the objective of posterior approximation as a supervised classification problem with a set-valued input: it repeatedly draws a task (or function) from the prior, draws a set of data points and their labels from it, masks one of the labels and learns to make probabilistic predictions for it based on the set-valued input of the rest of the data points. Presented with a set of samples from a new supervised learning task as input, PFNs make probabilistic predictions for arbitrary other data points in a single forward propagation, having learned to approximate Bayesian inference. We demonstrate that PFNs can near-perfectly mimic Gaussian processes and also enable efficient Bayesian inference for intractable problems, with over 200-fold speedups in multiple setups compared to current methods. We obtain strong results in very diverse areas such as Gaussian process regression, Bayesian neural networks, classification for small tabular data sets, and few-shot image classification, demonstrating the generality of PFNs. Code and trained PFNs are released at https://github.com/automl/TransformersCanDoBayesianInference.

State-of-the-art text-to-image models excel at photorealistic rendering but often struggle to capture the layout and object relationships implied by complex prompts. Scene graphs provide a natural structural prior, yet previous graph-guided approaches have typically relied on heavy GAN or diffusion pipelines, which lag behind modern autoregressive architectures in both speed and fidelity. We introduce SATURN (Structured Arrangement of Triplets for Unified Rendering Networks), a lightweight extension to VAR-CLIP that translates a scene graph into a salience-ordered token sequence, enabling a frozen CLIP-VQ-VAE backbone to interpret graph structure while fine-tuning only the VAR transformer. On the Visual Genome dataset, SATURN reduces FID from 56.45% to 21.62% and increases the Inception Score from 16.03 to 24.78, outperforming prior methods such as SG2IM and SGDiff without requiring extra modules or multi-stage training. Qualitative results further confirm improvements in object count fidelity and spatial relation accuracy, showing that SATURN effectively combines structural awareness with state-of-the-art autoregressive fidelity.

The Visual Question Answering (VQA) task requires the simultaneous understanding of image content and question semantics. However, existing methods often have difficulty handling complex reasoning scenarios due to insufficient cross-modal interaction and capturing the entity spatial relationships in the image.huang2023adaptiveliu2021comparingguibas2021adaptivezhang2022vsaWe studied a brand-new approach to replace the attention mechanism in order to enhance the reasoning ability of the model and its understanding of spatial relationships.Specifically, we propose a dynamic bidirectional spatial tower, which is divided into four layers to observe the image according to the principle of human gestalt vision. This naturally provides a powerful structural prior for the spatial organization between entities, enabling the model to no longer blindly search for relationships between pixels but make judgments based on more meaningful perceptual units. Change from "seeing images" to "perceiving and organizing image content".A large number of experiments have shown that our module can be used in any other multimodal model and achieve advanced results, demonstrating its potential in spatial relationship processing.Meanwhile, the multimodal visual question-answering model July trained by our method has achieved state-of-the-art results with only 3B parameters, especially on the question-answering dataset of spatial relations.

Multimodal Large Language Models have made significant strides in integrating visual and textual information, yet they often struggle with effectively aligning these modalities. We introduce a novel image tokenizer that bridges this gap by applying the principle of Byte-Pair Encoding (BPE) to visual data. Unlike conventional approaches that rely on separate visual encoders, our method directly incorporates structural prior information into image tokens, mirroring the successful tokenization strategies used in text-only Large Language Models. This innovative approach enables Transformer models to more effectively learn and reason across modalities. Through theoretical analysis and extensive experiments, we demonstrate that our BPE Image Tokenizer significantly enhances MLLMs' multimodal understanding capabilities, even with limited training data. Our method not only improves performance across various benchmarks but also shows promising scalability, potentially paving the way for more efficient and capable multimodal foundation models.

We present AvatarReX, a new method for learning NeRF-based full-body avatars from video data. The learnt avatar not only provides expressive control of the body, hands and the face together, but also supports real-time animation and rendering. To this end, we propose a compositional avatar representation, where the body, hands and the face are separately modeled in a way that the structural prior from parametric mesh templates is properly utilized without compromising representation flexibility. Furthermore, we disentangle the geometry and appearance for each part. With these technical designs, we propose a dedicated deferred rendering pipeline, which can be executed in real-time framerate to synthesize high-quality free-view images. The disentanglement of geometry and appearance also allows us to design a two-pass training strategy that combines volume rendering and surface rendering for network training. In this way, patch-level supervision can be applied to force the network to learn sharp appearance details on the basis of geometry estimation. Overall, our method enables automatic construction of expressive full-body avatars with real-time rendering capability, and can generate photo-realistic images with dynamic details for novel body motions and facial expressions.

From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Markov kernels) gives a nice framework for conceptualization and analysis of many aspects of machine learning. Using categorical methods, we construct models for parametric and nonparametric Bayesian reasoning on function spaces, thus providing a basis for the supervised learning problem. In particular, stochastic processes are arrows to these function spaces which serve as prior probabilities. The resulting inference maps can often be analytically constructed in this symmetric monoidal weakly closed category. We also show how to view general stochastic processes using functor categories and demonstrate the Kalman filter as an archetype for the hidden Markov model.

Most bandit algorithms assume that the reward variances or their upper bounds are known, and that they are the same for all arms. This naturally leads to suboptimal performance and higher regret due to variance overestimation. On the other hand, underestimated reward variances may lead to linear regret due to committing early to a suboptimal arm. This motivated prior works on variance-adaptive frequentist algorithms, which have strong instance-dependent regret bounds but cannot incorporate prior knowledge on reward variances. We lay foundations for the Bayesian setting, which incorporates prior knowledge. This results in lower regret in practice, due to using the prior in the algorithm design, and also improved regret guarantees. Specifically, we study Gaussian bandits with {unknown heterogeneous reward variances}, and develop a Thompson sampling algorithm with prior-dependent Bayes regret bounds. We achieve lower regret with lower reward variances and more informative priors on them, which is precisely why we pay only for what is uncertain. This is the first result of its kind. Finally, we corroborate our theory with extensive experiments, which show the superiority of our variance-adaptive Bayesian algorithm over prior frequentist approaches. We also show that our approach is robust to model misspecification and can be applied with estimated priors.

Diffusion models recently proved to be remarkable priors for Bayesian inverse problems. However, training these models typically requires access to large amounts of clean data, which could prove difficult in some settings. In this work, we present a novel method based on the expectation-maximization algorithm for training diffusion models from incomplete and noisy observations only. Unlike previous works, our method leads to proper diffusion models, which is crucial for downstream tasks. As part of our method, we propose and motivate an improved posterior sampling scheme for unconditional diffusion models. We present empirical evidence supporting the effectiveness of our method.

Text-to-3D generation by distilling pretrained large-scale text-to-image diffusion models has shown great promise but still suffers from inconsistent 3D geometric structures (Janus problems) and severe artifacts. The aforementioned problems mainly stem from 2D diffusion models lacking 3D awareness during the lifting. In this work, we present GeoDream, a novel method that incorporates explicit generalized 3D priors with 2D diffusion priors to enhance the capability of obtaining unambiguous 3D consistent geometric structures without sacrificing diversity or fidelity. Specifically, we first utilize a multi-view diffusion model to generate posed images and then construct cost volume from the predicted image, which serves as native 3D geometric priors, ensuring spatial consistency in 3D space. Subsequently, we further propose to harness 3D geometric priors to unlock the great potential of 3D awareness in 2D diffusion priors via a disentangled design. Notably, disentangling 2D and 3D priors allows us to refine 3D geometric priors further. We justify that the refined 3D geometric priors aid in the 3D-aware capability of 2D diffusion priors, which in turn provides superior guidance for the refinement of 3D geometric priors. Our numerical and visual comparisons demonstrate that GeoDream generates more 3D consistent textured meshes with high-resolution realistic renderings (i.e., 1024 times 1024) and adheres more closely to semantic coherence.

In recent years, the neural implicit surface has emerged as a powerful representation for multi-view surface reconstruction due to its simplicity and state-of-the-art performance. However, reconstructing smooth and detailed surfaces in indoor scenes from multi-view images presents unique challenges. Indoor scenes typically contain large texture-less regions, making the photometric loss unreliable for optimizing the implicit surface. Previous work utilizes monocular geometry priors to improve the reconstruction in indoor scenes. However, monocular priors often contain substantial errors in thin structure regions due to domain gaps and the inherent inconsistencies when derived independently from different views. This paper presents DebSDF to address these challenges, focusing on the utilization of uncertainty in monocular priors and the bias in SDF-based volume rendering. We propose an uncertainty modeling technique that associates larger uncertainties with larger errors in the monocular priors. High-uncertainty priors are then excluded from optimization to prevent bias. This uncertainty measure also informs an importance-guided ray sampling and adaptive smoothness regularization, enhancing the learning of fine structures. We further introduce a bias-aware signed distance function to density transformation that takes into account the curvature and the angle between the view direction and the SDF normals to reconstruct fine details better. Our approach has been validated through extensive experiments on several challenging datasets, demonstrating improved qualitative and quantitative results in reconstructing thin structures in indoor scenes, thereby outperforming previous work.

Inferring causal structure poses a combinatorial search problem that typically involves evaluating structures with a score or independence test. The resulting search is costly, and designing suitable scores or tests that capture prior knowledge is difficult. In this work, we propose to amortize causal structure learning. Rather than searching over structures, we train a variational inference model to directly predict the causal structure from observational or interventional data. This allows our inference model to acquire domain-specific inductive biases for causal discovery solely from data generated by a simulator, bypassing both the hand-engineering of suitable score functions and the search over graphs. The architecture of our inference model emulates permutation invariances that are crucial for statistical efficiency in structure learning, which facilitates generalization to significantly larger problem instances than seen during training. On synthetic data and semisynthetic gene expression data, our models exhibit robust generalization capabilities when subject to substantial distribution shifts and significantly outperform existing algorithms, especially in the challenging genomics domain. Our code and models are publicly available at: https://github.com/larslorch/avici.

Recent studies on inverse problems have proposed posterior samplers that leverage the pre-trained diffusion models as powerful priors. These attempts have paved the way for using diffusion models in a wide range of inverse problems. However, the existing methods entail computationally demanding iterative sampling procedures and optimize a separate solution for each measurement, which leads to limited scalability and lack of generalization capability across unseen samples. To address these limitations, we propose a novel approach, Diffusion prior-based Amortized Variational Inference (DAVI) that solves inverse problems with a diffusion prior from an amortized variational inference perspective. Specifically, instead of separate measurement-wise optimization, our amortized inference learns a function that directly maps measurements to the implicit posterior distributions of corresponding clean data, enabling a single-step posterior sampling even for unseen measurements. Extensive experiments on image restoration tasks, e.g., Gaussian deblur, 4times super-resolution, and box inpainting with two benchmark datasets, demonstrate our approach's superior performance over strong baselines. Code is available at https://github.com/mlvlab/DAVI.

We propose a novel hierarchical Bayesian model for learning with a large (possibly infinite) number of tasks/episodes, which suits well the few-shot meta learning problem. We consider episode-wise random variables to model episode-specific target generative processes, where these local random variables are governed by a higher-level global random variate. The global variable helps memorize the important information from historic episodes while controlling how much the model needs to be adapted to new episodes in a principled Bayesian manner. Within our model framework, the prediction on a novel episode/task can be seen as a Bayesian inference problem. However, a main obstacle in learning with a large/infinite number of local random variables in online nature, is that one is not allowed to store the posterior distribution of the current local random variable for frequent future updates, typical in conventional variational inference. We need to be able to treat each local variable as a one-time iterate in the optimization. We propose a Normal-Inverse-Wishart model, for which we show that this one-time iterate optimization becomes feasible due to the approximate closed-form solutions for the local posterior distributions. The resulting algorithm is more attractive than the MAML in that it is not required to maintain computational graphs for the whole gradient optimization steps per episode. Our approach is also different from existing Bayesian meta learning methods in that unlike dealing with a single random variable for the whole episodes, our approach has a hierarchical structure that allows one-time episodic optimization, desirable for principled Bayesian learning with many/infinite tasks. The code is available at https://github.com/minyoungkim21/niwmeta.

This study introduces PV-RNN, a novel variational RNN inspired by the predictive-coding ideas. The model learns to extract the probabilistic structures hidden in fluctuating temporal patterns by dynamically changing the stochasticity of its latent states. Its architecture attempts to address two major concerns of variational Bayes RNNs: how can latent variables learn meaningful representations and how can the inference model transfer future observations to the latent variables. PV-RNN does both by introducing adaptive vectors mirroring the training data, whose values can then be adapted differently during evaluation. Moreover, prediction errors during backpropagation, rather than external inputs during the forward computation, are used to convey information to the network about the external data. For testing, we introduce error regression for predicting unseen sequences as inspired by predictive coding that leverages those mechanisms. The model introduces a weighting parameter, the meta-prior, to balance the optimization pressure placed on two terms of a lower bound on the marginal likelihood of the sequential data. We test the model on two datasets with probabilistic structures and show that with high values of the meta-prior the network develops deterministic chaos through which the data's randomness is imitated. For low values, the model behaves as a random process. The network performs best on intermediate values, and is able to capture the latent probabilistic structure with good generalization. Analyzing the meta-prior's impact on the network allows to precisely study the theoretical value and practical benefits of incorporating stochastic dynamics in our model. We demonstrate better prediction performance on a robot imitation task with our model using error regression compared to a standard variational Bayes model lacking such a procedure.

Denoising diffusion probabilistic models have been recently proposed to generate high-quality samples by estimating the gradient of the data density. The framework defines the prior noise as a standard Gaussian distribution, whereas the corresponding data distribution may be more complicated than the standard Gaussian distribution, which potentially introduces inefficiency in denoising the prior noise into the data sample because of the discrepancy between the data and the prior. In this paper, we propose PriorGrad to improve the efficiency of the conditional diffusion model for speech synthesis (for example, a vocoder using a mel-spectrogram as the condition) by applying an adaptive prior derived from the data statistics based on the conditional information. We formulate the training and sampling procedures of PriorGrad and demonstrate the advantages of an adaptive prior through a theoretical analysis. Focusing on the speech synthesis domain, we consider the recently proposed diffusion-based speech generative models based on both the spectral and time domains and show that PriorGrad achieves faster convergence and inference with superior performance, leading to an improved perceptual quality and robustness to a smaller network capacity, and thereby demonstrating the efficiency of a data-dependent adaptive prior.

Various stuff and things in visual data possess specific traits, which can be learned by deep neural networks and are implicitly represented as the visual prior, e.g., object location and shape, in the model. Such prior potentially impacts many vision tasks. For example, in conditional image synthesis, spatial conditions failing to adhere to the prior can result in visually inaccurate synthetic results. This work aims to explicitly learn the visual prior and enable the customization of sampling. Inspired by advances in language modeling, we propose to learn Visual prior via Generative Pre-Training, dubbed VisorGPT. By discretizing visual locations of objects, e.g., bounding boxes, human pose, and instance masks, into sequences, \our~can model visual prior through likelihood maximization. Besides, prompt engineering is investigated to unify various visual locations and enable customized sampling of sequential outputs from the learned prior. Experimental results demonstrate that \our~can effectively model the visual prior, which can be employed for many vision tasks, such as customizing accurate human pose for conditional image synthesis models like ControlNet. Code will be released at https://github.com/Sierkinhane/VisorGPT.

The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restriction has a significant impact on the quality of inferences made using variational methods. We introduce a new approach for specifying flexible, arbitrarily complex and scalable approximate posterior distributions. Our approximations are distributions constructed through a normalizing flow, whereby a simple initial density is transformed into a more complex one by applying a sequence of invertible transformations until a desired level of complexity is attained. We use this view of normalizing flows to develop categories of finite and infinitesimal flows and provide a unified view of approaches for constructing rich posterior approximations. We demonstrate that the theoretical advantages of having posteriors that better match the true posterior, combined with the scalability of amortized variational approaches, provides a clear improvement in performance and applicability of variational inference.

Exposing meaningful and interpretable neural interactions is critical to understanding neural circuits. Inferred neural interactions from neural signals primarily reflect functional interactions. In a long experiment, subject animals may experience different stages defined by the experiment, stimuli, or behavioral states, and hence functional interactions can change over time. To model dynamically changing functional interactions, prior work employs state-switching generalized linear models with hidden Markov models (i.e., HMM-GLMs). However, we argue they lack biological plausibility, as functional interactions are shaped and confined by the underlying anatomical connectome. Here, we propose a novel prior-informed state-switching GLM. We introduce both a Gaussian prior and a one-hot prior over the GLM in each state. The priors are learnable. We will show that the learned prior should capture the state-constant interaction, shedding light on the underlying anatomical connectome and revealing more likely physical neuron interactions. The state-dependent interaction modeled by each GLM offers traceability to capture functional variations across multiple brain states. Our methods effectively recover true interaction structures in simulated data, achieve the highest predictive likelihood with real neural datasets, and render interaction structures and hidden states more interpretable when applied to real neural data.

Diffusion models have emerged as the new state-of-the-art generative model with high quality samples, with intriguing properties such as mode coverage and high flexibility. They have also been shown to be effective inverse problem solvers, acting as the prior of the distribution, while the information of the forward model can be granted at the sampling stage. Nonetheless, as the generative process remains in the same high dimensional (i.e. identical to data dimension) space, the models have not been extended to 3D inverse problems due to the extremely high memory and computational cost. In this paper, we combine the ideas from the conventional model-based iterative reconstruction with the modern diffusion models, which leads to a highly effective method for solving 3D medical image reconstruction tasks such as sparse-view tomography, limited angle tomography, compressed sensing MRI from pre-trained 2D diffusion models. In essence, we propose to augment the 2D diffusion prior with a model-based prior in the remaining direction at test time, such that one can achieve coherent reconstructions across all dimensions. Our method can be run in a single commodity GPU, and establishes the new state-of-the-art, showing that the proposed method can perform reconstructions of high fidelity and accuracy even in the most extreme cases (e.g. 2-view 3D tomography). We further reveal that the generalization capacity of the proposed method is surprisingly high, and can be used to reconstruct volumes that are entirely different from the training dataset.

We generalise an existing construction of Bayesian Lenses to admit lenses between pairs of objects where the backwards object is dependent on states on the forwards object (interpreted as probability distributions). This gives a natural setting for studying stochastic maps with Bayesian inverses restricted to the points supported by a given prior. In order to state this formally we develop a proposed definition by Fritz of a support object in a Markov category and show that these give rise to a section into the category of dependent Bayesian lenses encoding a more canonical notion of Bayesian inversion.

The distribution of the weights of modern deep neural networks (DNNs) - crucial for uncertainty quantification and robustness - is an eminently complex object due to its extremely high dimensionality. This paper proposes one of the first large-scale explorations of the posterior distribution of deep Bayesian Neural Networks (BNNs), expanding its study to real-world vision tasks and architectures. Specifically, we investigate the optimal approach for approximating the posterior, analyze the connection between posterior quality and uncertainty quantification, delve into the impact of modes on the posterior, and explore methods for visualizing the posterior. Moreover, we uncover weight-space symmetries as a critical aspect for understanding the posterior. To this extent, we develop an in-depth assessment of the impact of both permutation and scaling symmetries that tend to obfuscate the Bayesian posterior. While the first type of transformation is known for duplicating modes, we explore the relationship between the latter and L2 regularization, challenging previous misconceptions. Finally, to help the community improve our understanding of the Bayesian posterior, we will shortly release the first large-scale checkpoint dataset, including thousands of real-world models and our codes.

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are increasingly replaced by data-driven deep generative models, and several groups have recently shown that state-of-the-art score-based diffusion models yield particularly strong performance and flexibility. In this paper, we show that the powerful paradigm of posterior sampling with diffusion models can be extended to include rich, structured, noise models. To that end, we propose a joint conditional reverse diffusion process with learned scores for the noise and signal-generating distribution. We demonstrate strong performance gains across various inverse problems with structured noise, outperforming competitive baselines that use normalizing flows and adversarial networks. This opens up new opportunities and relevant practical applications of diffusion modeling for inverse problems in the context of non-Gaussian measurement models.

Model pre-training is essential in human-centric perception. In this paper, we first introduce masked image modeling (MIM) as a pre-training approach for this task. Upon revisiting the MIM training strategy, we reveal that human structure priors offer significant potential. Motivated by this insight, we further incorporate an intuitive human structure prior - human parts - into pre-training. Specifically, we employ this prior to guide the mask sampling process. Image patches, corresponding to human part regions, have high priority to be masked out. This encourages the model to concentrate more on body structure information during pre-training, yielding substantial benefits across a range of human-centric perception tasks. To further capture human characteristics, we propose a structure-invariant alignment loss that enforces different masked views, guided by the human part prior, to be closely aligned for the same image. We term the entire method as HAP. HAP simply uses a plain ViT as the encoder yet establishes new state-of-the-art performance on 11 human-centric benchmarks, and on-par result on one dataset. For example, HAP achieves 78.1% mAP on MSMT17 for person re-identification, 86.54% mA on PA-100K for pedestrian attribute recognition, 78.2% AP on MS COCO for 2D pose estimation, and 56.0 PA-MPJPE on 3DPW for 3D pose and shape estimation.

Learning causal structure from observational data often assumes that we observe independent and identically distributed (i.\,i.\,d) data. The traditional approach aims to find a graphical representation that encodes the same set of conditional independence relationships as those present in the observed distribution. It is known that under i.\,i.\,d assumption, even with infinite data, there is a limit to how fine-grained a causal structure we can identify. To overcome this limitation, recent work has explored using data originating from different, related environments to learn richer causal structure. These approaches implicitly rely on the independent causal mechanisms (ICM) principle, which postulates that the mechanism giving rise to an effect given its causes and the mechanism which generates the causes do not inform or influence each other. Thus, components of the causal model can independently change from environment to environment. Despite its wide application in machine learning and causal inference, there is a lack of statistical formalization of the ICM principle and how it enables identification of richer causal structures from grouped data. Here we present new causal de Finetti theorems which offer a first statistical formalization of ICM principle and show how causal structure identification is possible from exchangeable data. Our work provides theoretical justification for a broad range of techniques leveraging multi-environment data to learn causal structure.

Real-world single image denoising is crucial and practical in computer vision. Bayesian inversions combined with score priors now have proven effective for single image denoising but are limited to white Gaussian noise. Moreover, applying existing score-based methods for real-world denoising requires not only the explicit train of score priors on the target domain but also the careful design of sampling procedures for posterior inference, which is complicated and impractical. To address these limitations, we propose a score priors-guided deep variational inference, namely ScoreDVI, for practical real-world denoising. By considering the deep variational image posterior with a Gaussian form, score priors are extracted based on easily accessible minimum MSE Non-i.i.d Gaussian denoisers and variational samples, which in turn facilitate optimizing the variational image posterior. Such a procedure adaptively applies cheap score priors to denoising. Additionally, we exploit a Non-i.i.d Gaussian mixture model and variational noise posterior to model the real-world noise. This scheme also enables the pixel-wise fusion of multiple image priors and variational image posteriors. Besides, we develop a noise-aware prior assignment strategy that dynamically adjusts the weight of image priors in the optimization. Our method outperforms other single image-based real-world denoising methods and achieves comparable performance to dataset-based unsupervised methods.

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However, existing methods are often computationally expensive, or demand costly retraining when priors change, limiting their utility, particularly in sequential inference problems such as real-time sensor fusion. To address these challenges, we introduce the Distribution Transformer -- a novel architecture that can learn arbitrary distribution-to-distribution mappings. Our method can be trained to map a prior to the corresponding posterior, conditioned on some dataset -- thus performing approximate Bayesian inference. Our novel architecture represents a prior distribution as a (universally-approximating) Gaussian Mixture Model (GMM), and transforms it into a GMM representation of the posterior. The components of the GMM attend to each other via self-attention, and to the datapoints via cross-attention. We demonstrate that Distribution Transformers both maintain flexibility to vary the prior, and significantly reduces computation times-from minutes to milliseconds-while achieving log-likelihood performance on par with or superior to existing approximate inference methods across tasks such as sequential inference, quantum system parameter inference, and Gaussian Process predictive posterior inference with hyperpriors.

Prior-data fitted networks (PFNs) were recently proposed as a new paradigm for machine learning. Instead of training the network to an observed training set, a fixed model is pre-trained offline on small, simulated training sets from a variety of tasks. The pre-trained model is then used to infer class probabilities in-context on fresh training sets with arbitrary size and distribution. Empirically, PFNs achieve state-of-the-art performance on tasks with similar size to the ones used in pre-training. Surprisingly, their accuracy further improves when passed larger data sets during inference. This article establishes a theoretical foundation for PFNs and illuminates the statistical mechanisms governing their behavior. While PFNs are motivated by Bayesian ideas, a purely frequentistic interpretation of PFNs as pre-tuned, but untrained predictors explains their behavior. A predictor's variance vanishes if its sensitivity to individual training samples does and the bias vanishes only if it is appropriately localized around the test feature. The transformer architecture used in current PFN implementations ensures only the former. These findings shall prove useful for designing architectures with favorable empirical behavior.

We show that taking the width and depth to infinity in a deep neural network with skip connections, when branches are scaled by 1/depth (the only nontrivial scaling), result in the same covariance structure no matter how that limit is taken. This explains why the standard infinite-width-then-depth approach provides practical insights even for networks with depth of the same order as width. We also demonstrate that the pre-activations, in this case, have Gaussian distributions which has direct applications in Bayesian deep learning. We conduct extensive simulations that show an excellent match with our theoretical findings.

We present a diffusion-based model for 3D-aware generative novel view synthesis from as few as a single input image. Our model samples from the distribution of possible renderings consistent with the input and, even in the presence of ambiguity, is capable of rendering diverse and plausible novel views. To achieve this, our method makes use of existing 2D diffusion backbones but, crucially, incorporates geometry priors in the form of a 3D feature volume. This latent feature field captures the distribution over possible scene representations and improves our method's ability to generate view-consistent novel renderings. In addition to generating novel views, our method has the ability to autoregressively synthesize 3D-consistent sequences. We demonstrate state-of-the-art results on synthetic renderings and room-scale scenes; we also show compelling results for challenging, real-world objects.

Autoencoders and their variants are among the most widely used models in representation learning and generative modeling. However, autoencoder-based models usually assume that the learned representations are i.i.d. and fail to capture the correlations between the data samples. To address this issue, we propose a novel Sparse Gaussian Process Bayesian Autoencoder (SGPBAE) model in which we impose fully Bayesian sparse Gaussian Process priors on the latent space of a Bayesian Autoencoder. We perform posterior estimation for this model via stochastic gradient Hamiltonian Monte Carlo. We evaluate our approach qualitatively and quantitatively on a wide range of representation learning and generative modeling tasks and show that our approach consistently outperforms multiple alternatives relying on Variational Autoencoders.

With the growth of neural network size, model compression has attracted increasing interest in recent research. As one of the most common techniques, pruning has been studied for a long time. By exploiting the structured sparsity of the neural network, existing methods can prune neurons instead of individual weights. However, in most existing pruning methods, surviving neurons are randomly connected in the neural network without any structure, and the non-zero weights within each neuron are also randomly distributed. Such irregular sparse structure can cause very high control overhead and irregular memory access for the hardware and even increase the neural network computational complexity. In this paper, we propose a three-layer hierarchical prior to promote a more regular sparse structure during pruning. The proposed three-layer hierarchical prior can achieve per-neuron weight-level structured sparsity and neuron-level structured sparsity. We derive an efficient Turbo-variational Bayesian inferencing (Turbo-VBI) algorithm to solve the resulting model compression problem with the proposed prior. The proposed Turbo-VBI algorithm has low complexity and can support more general priors than existing model compression algorithms. Simulation results show that our proposed algorithm can promote a more regular structure in the pruned neural networks while achieving even better performance in terms of compression rate and inferencing accuracy compared with the baselines.

To achieve scalable and accurate inference for latent Gaussian processes, we propose a variational approximation based on a family of Gaussian distributions whose covariance matrices have sparse inverse Cholesky (SIC) factors. We combine this variational approximation of the posterior with a similar and efficient SIC-restricted Kullback-Leibler-optimal approximation of the prior. We then focus on a particular SIC ordering and nearest-neighbor-based sparsity pattern resulting in highly accurate prior and posterior approximations. For this setting, our variational approximation can be computed via stochastic gradient descent in polylogarithmic time per iteration. We provide numerical comparisons showing that the proposed double-Kullback-Leibler-optimal Gaussian-process approximation (DKLGP) can sometimes be vastly more accurate for stationary kernels than alternative approaches such as inducing-point and mean-field approximations at similar computational complexity.

We formalize constraint-based structure learning of the "true" causal graph from observed data when unobserved variables are also existent. We provide conditions for a "natural" family of constraint-based structure-learning algorithms that output graphs that are Markov equivalent to the causal graph. Under the faithfulness assumption, this natural family contains all exact structure-learning algorithms. We also provide a set of assumptions, under which any natural structure-learning algorithm outputs Markov equivalent graphs to the causal graph. These assumptions can be thought of as a relaxation of faithfulness, and most of them can be directly tested from (the underlying distribution) of the data, particularly when one focuses on structural causal models. We specialize the definitions and results for structural causal models.

Image synthesis under multi-modal priors is a useful and challenging task that has received increasing attention in recent years. A major challenge in using generative models to accomplish this task is the lack of paired data containing all modalities (i.e. priors) and corresponding outputs. In recent work, a variational auto-encoder (VAE) model was trained in a weakly supervised manner to address this challenge. Since the generative power of VAEs is usually limited, it is difficult for this method to synthesize images belonging to complex distributions. To this end, we propose a solution based on a denoising diffusion probabilistic models to synthesise images under multi-model priors. Based on the fact that the distribution over each time step in the diffusion model is Gaussian, in this work we show that there exists a closed-form expression to the generate the image corresponds to the given modalities. The proposed solution does not require explicit retraining for all modalities and can leverage the outputs of individual modalities to generate realistic images according to different constraints. We conduct studies on two real-world datasets to demonstrate the effectiveness of our approach

We present Bayesian Diffusion Models (BDM), a prediction algorithm that performs effective Bayesian inference by tightly coupling the top-down (prior) information with the bottom-up (data-driven) procedure via joint diffusion processes. We show the effectiveness of BDM on the 3D shape reconstruction task. Compared to prototypical deep learning data-driven approaches trained on paired (supervised) data-labels (e.g. image-point clouds) datasets, our BDM brings in rich prior information from standalone labels (e.g. point clouds) to improve the bottom-up 3D reconstruction. As opposed to the standard Bayesian frameworks where explicit prior and likelihood are required for the inference, BDM performs seamless information fusion via coupled diffusion processes with learned gradient computation networks. The specialty of our BDM lies in its capability to engage the active and effective information exchange and fusion of the top-down and bottom-up processes where each itself is a diffusion process. We demonstrate state-of-the-art results on both synthetic and real-world benchmarks for 3D shape reconstruction.

Generating high-quality 3D content requires models capable of learning robust distributions of complex scenes and the real-world objects within them. Recent Gaussian-based 3D reconstruction techniques have achieved impressive results in recovering high-fidelity 3D assets from sparse input images by predicting 3D Gaussians in a feed-forward manner. However, these techniques often lack the extensive priors and expressiveness offered by Diffusion Models. On the other hand, 2D Diffusion Models, which have been successfully applied to denoise multiview images, show potential for generating a wide range of photorealistic 3D outputs but still fall short on explicit 3D priors and consistency. In this work, we aim to bridge these two approaches by introducing DSplats, a novel method that directly denoises multiview images using Gaussian Splat-based Reconstructors to produce a diverse array of realistic 3D assets. To harness the extensive priors of 2D Diffusion Models, we incorporate a pretrained Latent Diffusion Model into the reconstructor backbone to predict a set of 3D Gaussians. Additionally, the explicit 3D representation embedded in the denoising network provides a strong inductive bias, ensuring geometrically consistent novel view generation. Our qualitative and quantitative experiments demonstrate that DSplats not only produces high-quality, spatially consistent outputs, but also sets a new standard in single-image to 3D reconstruction. When evaluated on the Google Scanned Objects dataset, DSplats achieves a PSNR of 20.38, an SSIM of 0.842, and an LPIPS of 0.109.

Stochastic gradient Markov Chain Monte Carlo (SGMCMC) is considered the gold standard for Bayesian inference in large-scale models, such as Bayesian neural networks. Since practitioners face speed versus accuracy tradeoffs in these models, variational inference (VI) is often the preferable option. Unfortunately, VI makes strong assumptions on both the factorization and functional form of the posterior. In this work, we propose a new non-parametric variational approximation that makes no assumptions about the approximate posterior's functional form and allows practitioners to specify the exact dependencies the algorithm should respect or break. The approach relies on a new Langevin-type algorithm that operates on a modified energy function, where parts of the latent variables are averaged over samples from earlier iterations of the Markov chain. This way, statistical dependencies can be broken in a controlled way, allowing the chain to mix faster. This scheme can be further modified in a "dropout" manner, leading to even more scalability. We test our scheme for ResNet-20 on CIFAR-10, SVHN, and FMNIST. In all cases, we find improvements in convergence speed and/or final accuracy compared to SG-MCMC and VI.

As a fundamental problem in computer vision, multi-view stereo (MVS) aims at recovering the 3D geometry of a target from a set of 2D images. Recent advances in MVS have shown that it is important to perceive non-local structured information for recovering geometry in low-textured areas. In this work, we propose a Hierarchical Prior Mining for Non-local Multi-View Stereo (HPM-MVS). The key characteristics are the following techniques that exploit non-local information to assist MVS: 1) A Non-local Extensible Sampling Pattern (NESP), which is able to adaptively change the size of sampled areas without becoming snared in locally optimal solutions. 2) A new approach to leverage non-local reliable points and construct a planar prior model based on K-Nearest Neighbor (KNN), to obtain potential hypotheses for the regions where prior construction is challenging. 3) A Hierarchical Prior Mining (HPM) framework, which is used to mine extensive non-local prior information at different scales to assist 3D model recovery, this strategy can achieve a considerable balance between the reconstruction of details and low-textured areas. Experimental results on the ETH3D and Tanks \& Temples have verified the superior performance and strong generalization capability of our method. Our code will be released.

Reconstructing 3D shapes from planar cross-sections is a challenge inspired by downstream applications like medical imaging and geographic informatics. The input is an in/out indicator function fully defined on a sparse collection of planes in space, and the output is an interpolation of the indicator function to the entire volume. Previous works addressing this sparse and ill-posed problem either produce low quality results, or rely on additional priors such as target topology, appearance information, or input normal directions. In this paper, we present OReX, a method for 3D shape reconstruction from slices alone, featuring a Neural Field as the interpolation prior. A modest neural network is trained on the input planes to return an inside/outside estimate for a given 3D coordinate, yielding a powerful prior that induces smoothness and self-similarities. The main challenge for this approach is high-frequency details, as the neural prior is overly smoothing. To alleviate this, we offer an iterative estimation architecture and a hierarchical input sampling scheme that encourage coarse-to-fine training, allowing the training process to focus on high frequencies at later stages. In addition, we identify and analyze a ripple-like effect stemming from the mesh extraction step. We mitigate it by regularizing the spatial gradients of the indicator function around input in/out boundaries during network training, tackling the problem at the root. Through extensive qualitative and quantitative experimentation, we demonstrate our method is robust, accurate, and scales well with the size of the input. We report state-of-the-art results compared to previous approaches and recent potential solutions, and demonstrate the benefit of our individual contributions through analysis and ablation studies.

Modeling latent variables with priors and hyperpriors is an essential problem in variational image compression. Formally, trade-off between rate and distortion is handled well if priors and hyperpriors precisely describe latent variables. Current practices only adopt univariate priors and process each variable individually. However, we find inter-correlations and intra-correlations exist when observing latent variables in a vectorized perspective. These findings reveal visual redundancies to improve rate-distortion performance and parallel processing ability to speed up compression. This encourages us to propose a novel vectorized prior. Specifically, a multivariate Gaussian mixture is proposed with means and covariances to be estimated. Then, a novel probabilistic vector quantization is utilized to effectively approximate means, and remaining covariances are further induced to a unified mixture and solved by cascaded estimation without context models involved. Furthermore, codebooks involved in quantization are extended to multi-codebooks for complexity reduction, which formulates an efficient compression procedure. Extensive experiments on benchmark datasets against state-of-the-art indicate our model has better rate-distortion performance and an impressive 3.18times compression speed up, giving us the ability to perform real-time, high-quality variational image compression in practice. Our source code is publicly available at https://github.com/xiaosu-zhu/McQuic.

In the stochastic multi-armed bandit problem, a randomized probability matching policy called Thompson sampling (TS) has shown excellent performance in various reward models. In addition to the empirical performance, TS has been shown to achieve asymptotic problem-dependent lower bounds in several models. However, its optimality has been mainly addressed under light-tailed or one-parameter models that belong to exponential families. In this paper, we consider the optimality of TS for the Pareto model that has a heavy tail and is parameterized by two unknown parameters. Specifically, we discuss the optimality of TS with probability matching priors that include the Jeffreys prior and the reference priors. We first prove that TS with certain probability matching priors can achieve the optimal regret bound. Then, we show the suboptimality of TS with other priors, including the Jeffreys and the reference priors. Nevertheless, we find that TS with the Jeffreys and reference priors can achieve the asymptotic lower bound if one uses a truncation procedure. These results suggest carefully choosing noninformative priors to avoid suboptimality and show the effectiveness of truncation procedures in TS-based policies.

Bayesian deep learning counts on the quality of posterior distribution estimation. However, the posterior of deep neural networks is highly multi-modal in nature, with local modes exhibiting varying generalization performance. Given a practical budget, targeting at the original posterior can lead to suboptimal performance, as some samples may become trapped in "bad" modes and suffer from overfitting. Leveraging the observation that "good" modes with low generalization error often reside in flat basins of the energy landscape, we propose to bias sampling on the posterior toward these flat regions. Specifically, we introduce an auxiliary guiding variable, the stationary distribution of which resembles a smoothed posterior free from sharp modes, to lead the MCMC sampler to flat basins. By integrating this guiding variable with the model parameter, we create a simple joint distribution that enables efficient sampling with minimal computational overhead. We prove the convergence of our method and further show that it converges faster than several existing flatness-aware methods in the strongly convex setting. Empirical results demonstrate that our method can successfully sample from flat basins of the posterior, and outperforms all compared baselines on multiple benchmarks including classification, calibration, and out-of-distribution detection.

Parameter inference, i.e. inferring the posterior distribution of the parameters of a statistical model given some data, is a central problem to many scientific disciplines. Generative models can be used as an alternative to Markov Chain Monte Carlo methods for conducting posterior inference, both in likelihood-based and simulation-based problems. However, assessing the accuracy of posteriors encoded in generative models is not straightforward. In this paper, we introduce `Tests of Accuracy with Random Points' (TARP) coverage testing as a method to estimate coverage probabilities of generative posterior estimators. Our method differs from previously-existing coverage-based methods, which require posterior evaluations. We prove that our approach is necessary and sufficient to show that a posterior estimator is accurate. We demonstrate the method on a variety of synthetic examples, and show that TARP can be used to test the results of posterior inference analyses in high-dimensional spaces. We also show that our method can detect inaccurate inferences in cases where existing methods fail.

In this work, we initiate the idea of using denoising diffusion models to learn priors for online decision making problems. Our special focus is on the meta-learning for bandit framework, with the goal of learning a strategy that performs well across bandit tasks of a same class. To this end, we train a diffusion model that learns the underlying task distribution and combine Thompson sampling with the learned prior to deal with new tasks at test time. Our posterior sampling algorithm is designed to carefully balance between the learned prior and the noisy observations that come from the learner's interaction with the environment. To capture realistic bandit scenarios, we also propose a novel diffusion model training procedure that trains even from incomplete and/or noisy data, which could be of independent interest. Finally, our extensive experimental evaluations clearly demonstrate the potential of the proposed approach.

Bayesian inference usually requires running potentially costly inference procedures separately for every new observation. In contrast, the idea of amortized Bayesian inference is to initially invest computational cost in training an inference network on simulated data, which can subsequently be used to rapidly perform inference (i.e., to return estimates of posterior distributions) for new observations. This approach has been applied to many real-world models in the sciences and engineering, but it is unclear how robust the approach is to adversarial perturbations in the observed data. Here, we study the adversarial robustness of amortized Bayesian inference, focusing on simulation-based estimation of multi-dimensional posterior distributions. We show that almost unrecognizable, targeted perturbations of the observations can lead to drastic changes in the predicted posterior and highly unrealistic posterior predictive samples, across several benchmark tasks and a real-world example from neuroscience. We propose a computationally efficient regularization scheme based on penalizing the Fisher information of the conditional density estimator, and show how it improves the adversarial robustness of amortized Bayesian inference.

Structured output representation is a generative task explored in computer vision that often times requires the mapping of low dimensional features to high dimensional structured outputs. Losses in complex spatial information in deterministic approaches such as Convolutional Neural Networks (CNN) lead to uncertainties and ambiguous structures within a single output representation. A probabilistic approach through deep Conditional Generative Models (CGM) is presented by Sohn et al. in which a particular model known as the Conditional Variational Auto-encoder (CVAE) is introduced and explored. While the original paper focuses on the task of image segmentation, this paper adopts the CVAE framework for the task of controlled output representation through attributes. This approach allows us to learn a disentangled multimodal prior distribution, resulting in more controlled and robust approach to sample generation. In this work we recreate the CVAE architecture and train it on images conditioned on various attributes obtained from two image datasets; the Large-scale CelebFaces Attributes (CelebA) dataset and the Caltech-UCSD Birds (CUB-200-2011) dataset. We attempt to generate new faces with distinct attributes such as hair color and glasses, as well as different bird species samples with various attributes. We further introduce strategies for improving generalized sample generation by applying a weighted term to the variational lower bound.

Recently, partial Bayesian neural networks (pBNNs), which only consider a subset of the parameters to be stochastic, were shown to perform competitively with full Bayesian neural networks. However, pBNNs are often multi-modal in the latent-variable space and thus challenging to approximate with parametric models. To address this problem, we propose an efficient sampling-based training strategy, wherein the training of a pBNN is formulated as simulating a Feynman--Kac model. We then describe variations of sequential Monte Carlo samplers that allow us to simultaneously estimate the parameters and the latent posterior distribution of this model at a tractable computational cost. We show on various synthetic and real-world datasets that our proposed training scheme outperforms the state of the art in terms of predictive performance.

Methods based on diffusion backbones have recently revolutionized novel view synthesis (NVS). However, those models require pretrained 2D diffusion checkpoints (e.g., Stable Diffusion) as the basis for geometrical priors. Since such checkpoints require exorbitant amounts of data and compute to train, this greatly limits the scalability of diffusion-based NVS models. We present Next-Scale Autoregression Conditioned by View (ArchonView), a method that significantly exceeds state-of-the-art methods despite being trained from scratch with 3D rendering data only and no 2D pretraining. We achieve this by incorporating both global (pose-augmented semantics) and local (multi-scale hierarchical encodings) conditioning into a backbone based on the next-scale autoregression paradigm. Our model also exhibits robust performance even for difficult camera poses where previous methods fail, and is several times faster in inference speed compared to diffusion. We experimentally verify that performance scales with model and dataset size, and conduct extensive demonstration of our method's synthesis quality across several tasks. Our code is open-sourced at https://github.com/Shiran-Yuan/ArchonView.

Approximations to Gaussian processes based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini batch-based learning. In this work, we address one limitation of sparse GPs, which is due to the challenge in dealing with a large number of inducing variables without imposing a special structure on the inducing inputs. In particular, we introduce a novel hierarchical prior, which imposes sparsity on the set of inducing variables. We treat our model variationally, and we experimentally show considerable computational gains compared to standard sparse GPs when sparsity on the inducing variables is realized considering the nearest inducing inputs of a random mini-batch of the data. We perform an extensive experimental validation that demonstrates the effectiveness of our approach compared to the state-of-the-art. Our approach enables the possibility to use sparse GPs using a large number of inducing points without incurring a prohibitive computational cost.

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

We aim to address sparse-view reconstruction of a 3D scene by leveraging priors from large-scale vision models. While recent advancements such as 3D Gaussian Splatting (3DGS) have demonstrated remarkable successes in 3D reconstruction, these methods typically necessitate hundreds of input images that densely capture the underlying scene, making them time-consuming and impractical for real-world applications. However, sparse-view reconstruction is inherently ill-posed and under-constrained, often resulting in inferior and incomplete outcomes. This is due to issues such as failed initialization, overfitting on input images, and a lack of details. To mitigate these challenges, we introduce LM-Gaussian, a method capable of generating high-quality reconstructions from a limited number of images. Specifically, we propose a robust initialization module that leverages stereo priors to aid in the recovery of camera poses and the reliable point clouds. Additionally, a diffusion-based refinement is iteratively applied to incorporate image diffusion priors into the Gaussian optimization process to preserve intricate scene details. Finally, we utilize video diffusion priors to further enhance the rendered images for realistic visual effects. Overall, our approach significantly reduces the data acquisition requirements compared to previous 3DGS methods. We validate the effectiveness of our framework through experiments on various public datasets, demonstrating its potential for high-quality 360-degree scene reconstruction. Visual results are on our website.

Bayesian models of cognition have gained considerable traction in computational neuroscience and psychiatry. Their scopes are now expected to expand rapidly to artificial intelligence, providing general inference frameworks to support embodied, adaptable, and energy-efficient autonomous agents. A central theory in this domain is predictive coding, which posits that learning and behaviour are driven by hierarchical probabilistic inferences about the causes of sensory inputs. Biological realism constrains these networks to rely on simple local computations in the form of precision-weighted predictions and prediction errors. This can make this framework highly efficient, but its implementation comes with unique challenges on the software development side. Embedding such models in standard neural network libraries often becomes limiting, as these libraries' compilation and differentiation backends can force a conceptual separation between optimization algorithms and the systems being optimized. This critically departs from other biological principles such as self-monitoring, self-organisation, cellular growth and functional plasticity. In this paper, we introduce pyhgf: a Python package backed by JAX and Rust for creating, manipulating and sampling dynamic networks for predictive coding. We improve over other frameworks by enclosing the network components as transparent, modular and malleable variables in the message-passing steps. The resulting graphs can implement arbitrary computational complexities as beliefs propagation. But the transparency of core variables can also translate into inference processes that leverage self-organisation principles, and express structure learning, meta-learning or causal discovery as the consequence of network structural adaptation to surprising inputs. The code, tutorials and documentation are hosted at: https://github.com/ilabcode/pyhgf.

Single image-to-3D generation is pivotal for crafting controllable 3D assets. Given its underconstrained nature, we leverage geometric priors from a 3D novel view generation diffusion model and appearance priors from a 2D image generation method to guide the optimization process. We note that a disparity exists between the training datasets of 2D and 3D diffusion models, leading to their outputs showing marked differences in appearance. Specifically, 2D models tend to deliver more detailed visuals, whereas 3D models produce consistent yet over-smooth results across different views. Hence, we optimize a set of 3D Gaussians using 3D priors in spatial domain to ensure geometric consistency, while exploiting 2D priors in the frequency domain through Fourier transform for higher visual quality. This 2D-3D hybrid Fourier Score Distillation objective function (dubbed hy-FSD), can be integrated into existing 3D generation methods, yielding significant performance improvements. With this technique, we further develop an image-to-3D generation pipeline to create high-quality 3D objects within one minute, named Fourier123. Extensive experiments demonstrate that Fourier123 excels in efficient generation with rapid convergence speed and visual-friendly generation results.

This paper proposes a Disentangled gEnerative cAusal Representation (DEAR) learning method under appropriate supervised information. Unlike existing disentanglement methods that enforce independence of the latent variables, we consider the general case where the underlying factors of interests can be causally related. We show that previous methods with independent priors fail to disentangle causally related factors even under supervision. Motivated by this finding, we propose a new disentangled learning method called DEAR that enables causal controllable generation and causal representation learning. The key ingredient of this new formulation is to use a structural causal model (SCM) as the prior distribution for a bidirectional generative model. The prior is then trained jointly with a generator and an encoder using a suitable GAN algorithm incorporated with supervised information on the ground-truth factors and their underlying causal structure. We provide theoretical justification on the identifiability and asymptotic convergence of the proposed method. We conduct extensive experiments on both synthesized and real data sets to demonstrate the effectiveness of DEAR in causal controllable generation, and the benefits of the learned representations for downstream tasks in terms of sample efficiency and distributional robustness.

We tackle the task of reconstructing hand-object interactions from short video clips. Given an input video, our approach casts 3D inference as a per-video optimization and recovers a neural 3D representation of the object shape, as well as the time-varying motion and hand articulation. While the input video naturally provides some multi-view cues to guide 3D inference, these are insufficient on their own due to occlusions and limited viewpoint variations. To obtain accurate 3D, we augment the multi-view signals with generic data-driven priors to guide reconstruction. Specifically, we learn a diffusion network to model the conditional distribution of (geometric) renderings of objects conditioned on hand configuration and category label, and leverage it as a prior to guide the novel-view renderings of the reconstructed scene. We empirically evaluate our approach on egocentric videos across 6 object categories, and observe significant improvements over prior single-view and multi-view methods. Finally, we demonstrate our system's ability to reconstruct arbitrary clips from YouTube, showing both 1st and 3rd person interactions.

Recent research has demonstrated that feature attribution methods for deep networks can themselves be incorporated into training; these attribution priors optimize for a model whose attributions have certain desirable properties -- most frequently, that particular features are important or unimportant. These attribution priors are often based on attribution methods that are not guaranteed to satisfy desirable interpretability axioms, such as completeness and implementation invariance. Here, we introduce attribution priors to optimize for higher-level properties of explanations, such as smoothness and sparsity, enabled by a fast new attribution method formulation called expected gradients that satisfies many important interpretability axioms. This improves model performance on many real-world tasks where previous attribution priors fail. Our experiments show that the gains from combining higher-level attribution priors with expected gradients attributions are consistent across image, gene expression, and health care data sets. We believe this work motivates and provides the necessary tools to support the widespread adoption of axiomatic attribution priors in many areas of applied machine learning. The implementations and our results have been made freely available to academic communities.

Computer vision methods that explicitly detect object parts and reason on them are a step towards inherently interpretable models. Existing approaches that perform part discovery driven by a fine-grained classification task make very restrictive assumptions on the geometric properties of the discovered parts; they should be small and compact. Although this prior is useful in some cases, in this paper we show that pre-trained transformer-based vision models, such as self-supervised DINOv2 ViT, enable the relaxation of these constraints. In particular, we find that a total variation (TV) prior, which allows for multiple connected components of any size, substantially outperforms previous work. We test our approach on three fine-grained classification benchmarks: CUB, PartImageNet and Oxford Flowers, and compare our results to previously published methods as well as a re-implementation of the state-of-the-art method PDiscoNet with a transformer-based backbone. We consistently obtain substantial improvements across the board, both on part discovery metrics and the downstream classification task, showing that the strong inductive biases in self-supervised ViT models require to rethink the geometric priors that can be used for unsupervised part discovery.

We present an algorithm for reconstructing dense, geometrically consistent depth for all pixels in a monocular video. We leverage a conventional structure-from-motion reconstruction to establish geometric constraints on pixels in the video. Unlike the ad-hoc priors in classical reconstruction, we use a learning-based prior, i.e., a convolutional neural network trained for single-image depth estimation. At test time, we fine-tune this network to satisfy the geometric constraints of a particular input video, while retaining its ability to synthesize plausible depth details in parts of the video that are less constrained. We show through quantitative validation that our method achieves higher accuracy and a higher degree of geometric consistency than previous monocular reconstruction methods. Visually, our results appear more stable. Our algorithm is able to handle challenging hand-held captured input videos with a moderate degree of dynamic motion. The improved quality of the reconstruction enables several applications, such as scene reconstruction and advanced video-based visual effects.

Recent work has shown promising results in causal discovery by leveraging interventional data with gradient-based methods, even when the intervened variables are unknown. However, previous work assumes that the correspondence between samples and interventions is known, which is often unrealistic. We envision a scenario with an extensive dataset sampled from multiple intervention distributions and one observation distribution, but where we do not know which distribution originated each sample and how the intervention affected the system, i.e., interventions are entirely latent. We propose a method based on neural networks and variational inference that addresses this scenario by framing it as learning a shared causal graph among an infinite mixture (under a Dirichlet process prior) of intervention structural causal models. Experiments with synthetic and real data show that our approach and its semi-supervised variant are able to discover causal relations in this challenging scenario.

We seek to understand fundamental tradeoffs between the accuracy of prior information that a learner has on a given problem and its learning performance. We introduce the notion of prioritized risk, which differs from traditional notions of minimax and Bayes risk by allowing us to study such fundamental tradeoffs in settings where reality does not necessarily conform to the learner's prior. We present a general reduction-based approach for extending classical minimax lower-bound techniques in order to lower bound the prioritized risk for statistical estimation problems. We also introduce a novel generalization of Fano's inequality (which may be of independent interest) for lower bounding the prioritized risk in more general settings involving unbounded losses. We illustrate the ability of our framework to provide insights into tradeoffs between prior information and learning performance for problems in estimation, regression, and reinforcement learning.

This paper proposes a new type of generative model that is able to quickly learn a latent representation without an encoder. This is achieved using empirical Bayes to calculate the expectation of the posterior, which is implemented by initialising a latent vector with zeros, then using the gradient of the log-likelihood of the data with respect to this zero vector as new latent points. The approach has similar characteristics to autoencoders, but with a simpler architecture, and is demonstrated in a variational autoencoder equivalent that permits sampling. This also allows implicit representation networks to learn a space of implicit functions without requiring a hypernetwork, retaining their representation advantages across datasets. The experiments show that the proposed method converges faster, with significantly lower reconstruction error than autoencoders, while requiring half the parameters.

Statistical shape modeling (SSM) enables population-based quantitative analysis of anatomical shapes, informing clinical diagnosis. Deep learning approaches predict correspondence-based SSM directly from unsegmented 3D images but require calibrated uncertainty quantification, motivating Bayesian formulations. Variational information bottleneck DeepSSM (VIB-DeepSSM) is an effective, principled framework for predicting probabilistic shapes of anatomy from images with aleatoric uncertainty quantification. However, VIB is only half-Bayesian and lacks epistemic uncertainty inference. We derive a fully Bayesian VIB formulation and demonstrate the efficacy of two scalable implementation approaches: concrete dropout and batch ensemble. Additionally, we introduce a novel combination of the two that further enhances uncertainty calibration via multimodal marginalization. Experiments on synthetic shapes and left atrium data demonstrate that the fully Bayesian VIB network predicts SSM from images with improved uncertainty reasoning without sacrificing accuracy.

Bayesian Neural Networks with Latent Variables (BNN+LVs) capture predictive uncertainty by explicitly modeling model uncertainty (via priors on network weights) and environmental stochasticity (via a latent input noise variable). In this work, we first show that BNN+LV suffers from a serious form of non-identifiability: explanatory power can be transferred between the model parameters and latent variables while fitting the data equally well. We demonstrate that as a result, in the limit of infinite data, the posterior mode over the network weights and latent variables is asymptotically biased away from the ground-truth. Due to this asymptotic bias, traditional inference methods may in practice yield parameters that generalize poorly and misestimate uncertainty. Next, we develop a novel inference procedure that explicitly mitigates the effects of likelihood non-identifiability during training and yields high-quality predictions as well as uncertainty estimates. We demonstrate that our inference method improves upon benchmark methods across a range of synthetic and real data-sets.

One method for obtaining generalizable solutions to machine learning tasks when presented with diverse training environments is to find invariant representations of the data. These are representations of the covariates such that the best model on top of the representation is invariant across training environments. In the context of linear Structural Equation Models (SEMs), invariant representations might allow us to learn models with out-of-distribution guarantees, i.e., models that are robust to interventions in the SEM. To address the invariant representation problem in a {\em finite sample} setting, we consider the notion of epsilon-approximate invariance. We study the following question: If a representation is approximately invariant with respect to a given number of training interventions, will it continue to be approximately invariant on a larger collection of unseen SEMs? This larger collection of SEMs is generated through a parameterized family of interventions. Inspired by PAC learning, we obtain finite-sample out-of-distribution generalization guarantees for approximate invariance that holds probabilistically over a family of linear SEMs without faithfulness assumptions. Our results show bounds that do not scale in ambient dimension when intervention sites are restricted to lie in a constant size subset of in-degree bounded nodes. We also show how to extend our results to a linear indirect observation model that incorporates latent variables.

Single-image 3D reconstruction remains a fundamental challenge in computer vision due to inherent geometric ambiguities and limited viewpoint information. Recent advances in Latent Video Diffusion Models (LVDMs) offer promising 3D priors learned from large-scale video data. However, leveraging these priors effectively faces three key challenges: (1) degradation in quality across large camera motions, (2) difficulties in achieving precise camera control, and (3) geometric distortions inherent to the diffusion process that damage 3D consistency. We address these challenges by proposing LiftImage3D, a framework that effectively releases LVDMs' generative priors while ensuring 3D consistency. Specifically, we design an articulated trajectory strategy to generate video frames, which decomposes video sequences with large camera motions into ones with controllable small motions. Then we use robust neural matching models, i.e. MASt3R, to calibrate the camera poses of generated frames and produce corresponding point clouds. Finally, we propose a distortion-aware 3D Gaussian splatting representation, which can learn independent distortions between frames and output undistorted canonical Gaussians. Extensive experiments demonstrate that LiftImage3D achieves state-of-the-art performance on two challenging datasets, i.e. LLFF, DL3DV, and Tanks and Temples, and generalizes well to diverse in-the-wild images, from cartoon illustrations to complex real-world scenes.

Recent 3D generation models typically rely on limited-scale 3D `gold-labels' or 2D diffusion priors for 3D content creation. However, their performance is upper-bounded by constrained 3D priors due to the lack of scalable learning paradigms. In this work, we present See3D, a visual-conditional multi-view diffusion model trained on large-scale Internet videos for open-world 3D creation. The model aims to Get 3D knowledge by solely Seeing the visual contents from the vast and rapidly growing video data -- You See it, You Got it. To achieve this, we first scale up the training data using a proposed data curation pipeline that automatically filters out multi-view inconsistencies and insufficient observations from source videos. This results in a high-quality, richly diverse, large-scale dataset of multi-view images, termed WebVi3D, containing 320M frames from 16M video clips. Nevertheless, learning generic 3D priors from videos without explicit 3D geometry or camera pose annotations is nontrivial, and annotating poses for web-scale videos is prohibitively expensive. To eliminate the need for pose conditions, we introduce an innovative visual-condition - a purely 2D-inductive visual signal generated by adding time-dependent noise to the masked video data. Finally, we introduce a novel visual-conditional 3D generation framework by integrating See3D into a warping-based pipeline for high-fidelity 3D generation. Our numerical and visual comparisons on single and sparse reconstruction benchmarks show that See3D, trained on cost-effective and scalable video data, achieves notable zero-shot and open-world generation capabilities, markedly outperforming models trained on costly and constrained 3D datasets. Please refer to our project page at: https://vision.baai.ac.cn/see3d

We study the sparse recovery problem with an underdetermined linear system characterized by a Kronecker-structured dictionary and a Kronecker-supported sparse vector. We cast this problem into the sparse Bayesian learning (SBL) framework and rely on the expectation-maximization method for a solution. To this end, we model the Kronecker-structured support with a hierarchical Gaussian prior distribution parameterized by a Kronecker-structured hyperparameter, leading to a non-convex optimization problem. The optimization problem is solved using the alternating minimization (AM) method and a singular value decomposition (SVD)-based method, resulting in two algorithms. Further, we analytically guarantee that the AM-based method converges to the stationary point of the SBL cost function. The SVD-based method, though it adopts approximations, is empirically shown to be more efficient and accurate. We then apply our algorithm to estimate the uplink wireless channel in an intelligent reflecting surface-aided MIMO system and extend the AM-based algorithm to address block sparsity in the channel. We also study the SBL cost to show that the minima of the cost function are achieved at sparse solutions and that incorporating the Kronecker structure reduces the number of local minima of the SBL cost function. Our numerical results demonstrate the effectiveness of our algorithms compared to the state-of-the-art.

We develop a novel method for carrying out model selection for Bayesian autoencoders (BAEs) by means of prior hyper-parameter optimization. Inspired by the common practice of type-II maximum likelihood optimization and its equivalence to Kullback-Leibler divergence minimization, we propose to optimize the distributional sliced-Wasserstein distance (DSWD) between the output of the autoencoder and the empirical data distribution. The advantages of this formulation are that we can estimate the DSWD based on samples and handle high-dimensional problems. We carry out posterior estimation of the BAE parameters via stochastic gradient Hamiltonian Monte Carlo and turn our BAE into a generative model by fitting a flexible Dirichlet mixture model in the latent space. Consequently, we obtain a powerful alternative to variational autoencoders, which are the preferred choice in modern applications of autoencoders for representation learning with uncertainty. We evaluate our approach qualitatively and quantitatively using a vast experimental campaign on a number of unsupervised learning tasks and show that, in small-data regimes where priors matter, our approach provides state-of-the-art results, outperforming multiple competitive baselines.

We present a general causal generative modelling framework for accurate estimation of high fidelity image counterfactuals with deep structural causal models. Estimation of interventional and counterfactual queries for high-dimensional structured variables, such as images, remains a challenging task. We leverage ideas from causal mediation analysis and advances in generative modelling to design new deep causal mechanisms for structured variables in causal models. Our experiments demonstrate that our proposed mechanisms are capable of accurate abduction and estimation of direct, indirect and total effects as measured by axiomatic soundness of counterfactuals.

Large Vision-Language Models (LVLMs) have demonstrated outstanding performance across various multimodal tasks. However, they suffer from a problem known as language prior, where responses are generated based solely on textual patterns while disregarding image information. Addressing the issue of language prior is crucial, as it can lead to undesirable biases or hallucinations when dealing with images that are out of training distribution. Despite its importance, current methods for accurately measuring language priors in LVLMs are poorly studied. Although existing benchmarks based on counterfactual or out-of-distribution images can partially be used to measure language priors, they fail to disentangle language priors from other confounding factors. To this end, we propose a new benchmark called VLind-Bench, which is the first benchmark specifically designed to measure the language priors, or blindness, of LVLMs. It not only includes tests on counterfactual images to assess language priors but also involves a series of tests to evaluate more basic capabilities such as commonsense knowledge, visual perception, and commonsense biases. For each instance in our benchmark, we ensure that all these basic tests are passed before evaluating the language priors, thereby minimizing the influence of other factors on the assessment. The evaluation and analysis of recent LVLMs in our benchmark reveal that almost all models exhibit a significant reliance on language priors, presenting a strong challenge in the field.

We consider the stochastic linear contextual bandit problem with high-dimensional features. We analyze the Thompson sampling algorithm using special classes of sparsity-inducing priors (e.g., spike-and-slab) to model the unknown parameter and provide a nearly optimal upper bound on the expected cumulative regret. To the best of our knowledge, this is the first work that provides theoretical guarantees of Thompson sampling in high-dimensional and sparse contextual bandits. For faster computation, we use variational inference instead of Markov Chain Monte Carlo (MCMC) to approximate the posterior distribution. Extensive simulations demonstrate the improved performance of our proposed algorithm over existing ones.

Reconstructing 3D objects from extremely sparse views is a long-standing and challenging problem. While recent techniques employ image diffusion models for generating plausible images at novel viewpoints or for distilling pre-trained diffusion priors into 3D representations using score distillation sampling (SDS), these methods often struggle to simultaneously achieve high-quality, consistent, and detailed results for both novel-view synthesis (NVS) and geometry. In this work, we present Sparse3D, a novel 3D reconstruction method tailored for sparse view inputs. Our approach distills robust priors from a multiview-consistent diffusion model to refine a neural radiance field. Specifically, we employ a controller that harnesses epipolar features from input views, guiding a pre-trained diffusion model, such as Stable Diffusion, to produce novel-view images that maintain 3D consistency with the input. By tapping into 2D priors from powerful image diffusion models, our integrated model consistently delivers high-quality results, even when faced with open-world objects. To address the blurriness introduced by conventional SDS, we introduce the category-score distillation sampling (C-SDS) to enhance detail. We conduct experiments on CO3DV2 which is a multi-view dataset of real-world objects. Both quantitative and qualitative evaluations demonstrate that our approach outperforms previous state-of-the-art works on the metrics regarding NVS and geometry reconstruction.

Contrastively trained encoders have recently been proven to invert the data-generating process: they encode each input, e.g., an image, into the true latent vector that generated the image (Zimmermann et al., 2021). However, real-world observations often have inherent ambiguities. For instance, images may be blurred or only show a 2D view of a 3D object, so multiple latents could have generated them. This makes the true posterior for the latent vector probabilistic with heteroscedastic uncertainty. In this setup, we extend the common InfoNCE objective and encoders to predict latent distributions instead of points. We prove that these distributions recover the correct posteriors of the data-generating process, including its level of aleatoric uncertainty, up to a rotation of the latent space. In addition to providing calibrated uncertainty estimates, these posteriors allow the computation of credible intervals in image retrieval. They comprise images with the same latent as a given query, subject to its uncertainty. Code is available at https://github.com/mkirchhof/Probabilistic_Contrastive_Learning

Partial differential equations (PDEs) are important tools to model physical systems, and including them into machine learning models is an important way of incorporating physical knowledge. Given any system of linear PDEs with constant coefficients, we propose a family of Gaussian process (GP) priors, which we call EPGP, such that all realizations are exact solutions of this system. We apply the Ehrenpreis-Palamodov fundamental principle, which works like a non-linear Fourier transform, to construct GP kernels mirroring standard spectral methods for GPs. Our approach can infer probable solutions of linear PDE systems from any data such as noisy measurements, or pointwise defined initial and boundary conditions. Constructing EPGP-priors is algorithmic, generally applicable, and comes with a sparse version (S-EPGP) that learns the relevant spectral frequencies and works better for big data sets. We demonstrate our approach on three families of systems of PDE, the heat equation, wave equation, and Maxwell's equations, where we improve upon the state of the art in computation time and precision, in some experiments by several orders of magnitude.

The infinitely wide neural network has been proven a useful and manageable mathematical model that enables the understanding of many phenomena appearing in deep learning. One example is the convergence of random deep networks to Gaussian processes that allows a rigorous analysis of the way the choice of activation function and network weights impacts the training dynamics. In this paper, we extend the seminal proof of Matthews et al. (2018) to a larger class of initial weight distributions (which we call PSEUDO-IID), including the established cases of IID and orthogonal weights, as well as the emerging low-rank and structured sparse settings celebrated for their computational speed-up benefits. We show that fully-connected and convolutional networks initialized with PSEUDO-IID distributions are all effectively equivalent up to their variance. Using our results, one can identify the Edge-of-Chaos for a broader class of neural networks and tune them at criticality in order to enhance their training. Moreover, they enable the posterior distribution of Bayesian Neural Networks to be tractable across these various initialization schemes.

Inspired by the foundational works by Spivak and Fong and Cruttwell et al., we introduce a categorical framework to formalize Bayesian inference and learning. The two key ideas at play here are the notions of Bayesian inversions and the functor GL as constructed by Cruttwell et al.. In this context, we find that Bayesian learning is the simplest case of the learning paradigm. We then obtain categorical formulations of batch and sequential Bayes updates while also verifying that the two coincide in a specific example.

Learning curve extrapolation aims to predict model performance in later epochs of training, based on the performance in earlier epochs. In this work, we argue that, while the inherent uncertainty in the extrapolation of learning curves warrants a Bayesian approach, existing methods are (i) overly restrictive, and/or (ii) computationally expensive. We describe the first application of prior-data fitted neural networks (PFNs) in this context. A PFN is a transformer, pre-trained on data generated from a prior, to perform approximate Bayesian inference in a single forward pass. We propose LC-PFN, a PFN trained to extrapolate 10 million artificial right-censored learning curves generated from a parametric prior proposed in prior art using MCMC. We demonstrate that LC-PFN can approximate the posterior predictive distribution more accurately than MCMC, while being over 10 000 times faster. We also show that the same LC-PFN achieves competitive performance extrapolating a total of 20 000 real learning curves from four learning curve benchmarks (LCBench, NAS-Bench-201, Taskset, and PD1) that stem from training a wide range of model architectures (MLPs, CNNs, RNNs, and Transformers) on 53 different datasets with varying input modalities (tabular, image, text, and protein data). Finally, we investigate its potential in the context of model selection and find that a simple LC-PFN based predictive early stopping criterion obtains 2 - 6x speed-ups on 45 of these datasets, at virtually no overhead.

We marry ideas from deep neural networks and approximate Bayesian inference to derive a generalised class of deep, directed generative models, endowed with a new algorithm for scalable inference and learning. Our algorithm introduces a recognition model to represent approximate posterior distributions, and that acts as a stochastic encoder of the data. We develop stochastic back-propagation -- rules for back-propagation through stochastic variables -- and use this to develop an algorithm that allows for joint optimisation of the parameters of both the generative and recognition model. We demonstrate on several real-world data sets that the model generates realistic samples, provides accurate imputations of missing data and is a useful tool for high-dimensional data visualisation.

Camera pose estimation is a long-standing computer vision problem that to date often relies on classical methods, such as handcrafted keypoint matching, RANSAC and bundle adjustment. In this paper, we propose to formulate the Structure from Motion (SfM) problem inside a probabilistic diffusion framework, modelling the conditional distribution of camera poses given input images. This novel view of an old problem has several advantages. (i) The nature of the diffusion framework mirrors the iterative procedure of bundle adjustment. (ii) The formulation allows a seamless integration of geometric constraints from epipolar geometry. (iii) It excels in typically difficult scenarios such as sparse views with wide baselines. (iv) The method can predict intrinsics and extrinsics for an arbitrary amount of images. We demonstrate that our method PoseDiffusion significantly improves over the classic SfM pipelines and the learned approaches on two real-world datasets. Finally, it is observed that our method can generalize across datasets without further training. Project page: https://posediffusion.github.io/

The objective for establishing dense correspondence between paired images consists of two terms: a data term and a prior term. While conventional techniques focused on defining hand-designed prior terms, which are difficult to formulate, recent approaches have focused on learning the data term with deep neural networks without explicitly modeling the prior, assuming that the model itself has the capacity to learn an optimal prior from a large-scale dataset. The performance improvement was obvious, however, they often fail to address inherent ambiguities of matching, such as textureless regions, repetitive patterns, and large displacements. To address this, we propose DiffMatch, a novel conditional diffusion-based framework designed to explicitly model both the data and prior terms. Unlike previous approaches, this is accomplished by leveraging a conditional denoising diffusion model. DiffMatch consists of two main components: conditional denoising diffusion module and cost injection module. We stabilize the training process and reduce memory usage with a stage-wise training strategy. Furthermore, to boost performance, we introduce an inference technique that finds a better path to the accurate matching field. Our experimental results demonstrate significant performance improvements of our method over existing approaches, and the ablation studies validate our design choices along with the effectiveness of each component. Project page is available at https://ku-cvlab.github.io/DiffMatch/.

Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach called Type II maximum likelihood or ML-II). An alternative learning procedure is to infer the posterior over hyperparameters in a hierarchical specification of GPs we call Fully Bayesian Gaussian Process Regression (GPR). This work considers two approximation schemes for the intractable hyperparameter posterior: 1) Hamiltonian Monte Carlo (HMC) yielding a sampling-based approximation and 2) Variational Inference (VI) where the posterior over hyperparameters is approximated by a factorized Gaussian (mean-field) or a full-rank Gaussian accounting for correlations between hyperparameters. We analyze the predictive performance for fully Bayesian GPR on a range of benchmark data sets.

Bayesian Optimization (BO) is typically used to optimize an unknown function f that is noisy and costly to evaluate, by exploiting an acquisition function that must be maximized at each optimization step. Even if provably asymptotically optimal BO algorithms are efficient at optimizing low-dimensional functions, scaling them to high-dimensional spaces remains an open problem, often tackled by assuming an additive structure for f. By doing so, BO algorithms typically introduce additional restrictive assumptions on the additive structure that reduce their applicability domain. This paper contains two main contributions: (i) we relax the restrictive assumptions on the additive structure of f without weakening the maximization guarantees of the acquisition function, and (ii) we address the over-exploration problem for decentralized BO algorithms. To these ends, we propose DuMBO, an asymptotically optimal decentralized BO algorithm that achieves very competitive performance against state-of-the-art BO algorithms, especially when the additive structure of f comprises high-dimensional factors.

Score-based Generative Models (SGMs) have achieved state-of-the-art synthesis results on diverse tasks. However, the current design space of the forward diffusion process is largely unexplored and often relies on physical intuition or simplifying assumptions. Leveraging results from the design of scalable Bayesian posterior samplers, we present a complete recipe for constructing forward processes in SGMs, all of which are guaranteed to converge to the target distribution of interest. We show that several existing SGMs can be cast as specific instantiations of this parameterization. Furthermore, building on this recipe, we construct a novel SGM: Phase Space Langevin Diffusion (PSLD), which performs score-based modeling in a space augmented with auxiliary variables akin to a physical phase space. We show that PSLD outperforms competing baselines in terms of sample quality and the speed-vs-quality tradeoff across different samplers on various standard image synthesis benchmarks. Moreover, we show that PSLD achieves sample quality comparable to state-of-the-art SGMs (FID: 2.10 on unconditional CIFAR-10 generation), providing an attractive alternative as an SGM backbone for further development. We will publish our code and model checkpoints for reproducibility at https://github.com/mandt-lab/PSLD.

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may observe that the inversion of the whole can be computed piecewise in terms of the component processes. We study the structure of this compositional rule, noting that it relates to the lens pattern in functional programming. Working in a suitably general axiomatic presentation of a category of Markov kernels, we see how we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a fibred category. We discuss the compositional nature of this, formulated as a functor on the underlying category and explore how this can used for a more type-driven approach to statistical inference.

In this paper, we study the problem of inference in high-order structured prediction tasks. In the context of Markov random fields, the goal of a high-order inference task is to maximize a score function on the space of labels, and the score function can be decomposed into sum of unary and high-order potentials. We apply a generative model approach to study the problem of high-order inference, and provide a two-stage convex optimization algorithm for exact label recovery. We also provide a new class of hypergraph structural properties related to hyperedge expansion that drives the success in general high-order inference problems. Finally, we connect the performance of our algorithm and the hyperedge expansion property using a novel hypergraph Cheeger-type inequality.

We present InterHandGen, a novel framework that learns the generative prior of two-hand interaction. Sampling from our model yields plausible and diverse two-hand shapes in close interaction with or without an object. Our prior can be incorporated into any optimization or learning methods to reduce ambiguity in an ill-posed setup. Our key observation is that directly modeling the joint distribution of multiple instances imposes high learning complexity due to its combinatorial nature. Thus, we propose to decompose the modeling of joint distribution into the modeling of factored unconditional and conditional single instance distribution. In particular, we introduce a diffusion model that learns the single-hand distribution unconditional and conditional to another hand via conditioning dropout. For sampling, we combine anti-penetration and classifier-free guidance to enable plausible generation. Furthermore, we establish the rigorous evaluation protocol of two-hand synthesis, where our method significantly outperforms baseline generative models in terms of plausibility and diversity. We also demonstrate that our diffusion prior can boost the performance of two-hand reconstruction from monocular in-the-wild images, achieving new state-of-the-art accuracy.

Current methods for performing 3D reconstruction and novel view synthesis (NVS) in ultrasound imaging data often face severe artifacts when training NeRF-based approaches. The artifacts produced by current approaches differ from NeRF floaters in general scenes because of the unique nature of ultrasound capture. Furthermore, existing models fail to produce reasonable 3D reconstructions when ultrasound data is captured or obtained casually in uncontrolled environments, which is common in clinical settings. Consequently, existing reconstruction and NVS methods struggle to handle ultrasound motion, fail to capture intricate details, and cannot model transparent and reflective surfaces. In this work, we introduced NeRF-US, which incorporates 3D-geometry guidance for border probability and scattering density into NeRF training, while also utilizing ultrasound-specific rendering over traditional volume rendering. These 3D priors are learned through a diffusion model. Through experiments conducted on our new "Ultrasound in the Wild" dataset, we observed accurate, clinically plausible, artifact-free reconstructions.

Hamiltonian Monte Carlo (HMC) is a powerful algorithm to sample latent variables from Bayesian models. The advent of probabilistic programming languages (PPLs) frees users from writing inference algorithms and lets users focus on modeling. However, many models are difficult for HMC to solve directly, and often require tricks like model reparameterization. We are motivated by the fact that many of those models could be simplified by marginalization. We propose to use automatic marginalization as part of the sampling process using HMC in a graphical model extracted from a PPL, which substantially improves sampling from real-world hierarchical models.

Biological systems perceive the world by simultaneously processing high-dimensional inputs from modalities as diverse as vision, audition, touch, proprioception, etc. The perception models used in deep learning on the other hand are designed for individual modalities, often relying on domain-specific assumptions such as the local grid structures exploited by virtually all existing vision models. These priors introduce helpful inductive biases, but also lock models to individual modalities. In this paper we introduce the Perceiver - a model that builds upon Transformers and hence makes few architectural assumptions about the relationship between its inputs, but that also scales to hundreds of thousands of inputs, like ConvNets. The model leverages an asymmetric attention mechanism to iteratively distill inputs into a tight latent bottleneck, allowing it to scale to handle very large inputs. We show that this architecture is competitive with or outperforms strong, specialized models on classification tasks across various modalities: images, point clouds, audio, video, and video+audio. The Perceiver obtains performance comparable to ResNet-50 and ViT on ImageNet without 2D convolutions by directly attending to 50,000 pixels. It is also competitive in all modalities in AudioSet.

In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the co-Kleisli category under the comonad (Omega x -) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identity-on-objects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood

We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." We explore how to interpret uncertain evidence, and by extension the importance of proper interpretation as it pertains to inference about latent variables. We consider a recently-proposed method "distributional evidence" as well as revisit two older methods: Jeffrey's rule and virtual evidence. We devise guidelines on how to account for uncertain evidence and we provide new insights, particularly regarding consistency. To showcase the impact of different interpretations of the same uncertain evidence, we carry out experiments in which one interpretation is defined as "correct." We then compare inference results from each different interpretation illustrating the importance of careful consideration of uncertain evidence.

Popular approaches for quantifying predictive uncertainty in deep neural networks often involve distributions over weights or multiple models, for instance via Markov Chain sampling, ensembling, or Monte Carlo dropout. These techniques usually incur overhead by having to train multiple model instances or do not produce very diverse predictions. This comprehensive and extensive survey aims to familiarize the reader with an alternative class of models based on the concept of Evidential Deep Learning: For unfamiliar data, they aim to admit "what they don't know", and fall back onto a prior belief. Furthermore, they allow uncertainty estimation in a single model and forward pass by parameterizing distributions over distributions. This survey recapitulates existing works, focusing on the implementation in a classification setting, before surveying the application of the same paradigm to regression. We also reflect on the strengths and weaknesses compared to other existing methods and provide the most fundamental derivations using a unified notation to aid future research.

Automatic text-to-3D synthesis has achieved remarkable advancements through the optimization of 3D models. Existing methods commonly rely on pre-trained text-to-image generative models, such as diffusion models, providing scores for 2D renderings of Neural Radiance Fields (NeRFs) and being utilized for optimizing NeRFs. However, these methods often encounter artifacts and inconsistencies across multiple views due to their limited understanding of 3D geometry. To address these limitations, we propose a reformulation of the optimization loss using the diffusion prior. Furthermore, we introduce a novel training approach that unlocks the potential of the diffusion prior. To improve 3D geometry representation, we apply auxiliary depth supervision for NeRF-rendered images and regularize the density field of NeRFs. Extensive experiments demonstrate the superiority of our method over prior works, resulting in advanced photo-realism and improved multi-view consistency.

Multiple types of inference are available for probabilistic graphical models, e.g., marginal, maximum-a-posteriori, and even marginal maximum-a-posteriori. Which one do researchers mean when they talk about ``planning as inference''? There is no consistency in the literature, different types are used, and their ability to do planning is further entangled with specific approximations or additional constraints. In this work we use the variational framework to show that, just like all commonly used types of inference correspond to different weightings of the entropy terms in the variational problem, planning corresponds exactly to a different set of weights. This means that all the tricks of variational inference are readily applicable to planning. We develop an analogue of loopy belief propagation that allows us to perform approximate planning in factored-state Markov decisions processes without incurring intractability due to the exponentially large state space. The variational perspective shows that the previous types of inference for planning are only adequate in environments with low stochasticity, and allows us to characterize each type by its own merits, disentangling the type of inference from the additional approximations that its practical use requires. We validate these results empirically on synthetic MDPs and tasks posed in the International Planning Competition.

Bayesian approaches for learning deep neural networks (BNN) have been received much attention and successfully applied to various applications. Particularly, BNNs have the merit of having better generalization ability as well as better uncertainty quantification. For the success of BNN, search an appropriate architecture of the neural networks is an important task, and various algorithms to find good sparse neural networks have been proposed. In this paper, we propose a new node-sparse BNN model which has good theoretical properties and is computationally feasible. We prove that the posterior concentration rate to the true model is near minimax optimal and adaptive to the smoothness of the true model. In particular the adaptiveness is the first of its kind for node-sparse BNNs. In addition, we develop a novel MCMC algorithm which makes the Bayesian inference of the node-sparse BNN model feasible in practice.

A Neural Process (NP) estimates a stochastic process implicitly defined with neural networks given a stream of data, rather than pre-specifying priors already known, such as Gaussian processes. An ideal NP would learn everything from data without any inductive biases, but in practice, we often restrict the class of stochastic processes for the ease of estimation. One such restriction is the use of a finite-dimensional latent variable accounting for the uncertainty in the functions drawn from NPs. Some recent works show that this can be improved with more "data-driven" source of uncertainty such as bootstrapping. In this work, we take a different approach based on the martingale posterior, a recently developed alternative to Bayesian inference. For the martingale posterior, instead of specifying prior-likelihood pairs, a predictive distribution for future data is specified. Under specific conditions on the predictive distribution, it can be shown that the uncertainty in the generated future data actually corresponds to the uncertainty of the implicitly defined Bayesian posteriors. Based on this result, instead of assuming any form of the latent variables, we equip a NP with a predictive distribution implicitly defined with neural networks and use the corresponding martingale posteriors as the source of uncertainty. The resulting model, which we name as Martingale Posterior Neural Process (MPNP), is demonstrated to outperform baselines on various tasks.

In the field of decision trees, most previous studies have difficulty ensuring the statistical optimality of a prediction of new data and suffer from overfitting because trees are usually used only to represent prediction functions to be constructed from given data. In contrast, some studies, including this paper, used the trees to represent stochastic data observation processes behind given data. Moreover, they derived the statistically optimal prediction, which is robust against overfitting, based on the Bayesian decision theory by assuming a prior distribution for the trees. However, these studies still have a problem in computing this Bayes optimal prediction because it involves an infeasible summation for all division patterns of a feature space, which is represented by the trees and some parameters. In particular, an open problem is a summation with respect to combinations of division axes, i.e., the assignment of features to inner nodes of the tree. We solve this by a Markov chain Monte Carlo method, whose step size is adaptively tuned according to a posterior distribution for the trees.

Given time series data, how can we answer questions like "what will happen in the future?" and "how did we get here?" These sorts of probabilistic inference questions are challenging when observations are high-dimensional. In this paper, we show how these questions can have compact, closed form solutions in terms of learned representations. The key idea is to apply a variant of contrastive learning to time series data. Prior work already shows that the representations learned by contrastive learning encode a probability ratio. By extending prior work to show that the marginal distribution over representations is Gaussian, we can then prove that joint distribution of representations is also Gaussian. Taken together, these results show that representations learned via temporal contrastive learning follow a Gauss-Markov chain, a graphical model where inference (e.g., prediction, planning) over representations corresponds to inverting a low-dimensional matrix. In one special case, inferring intermediate representations will be equivalent to interpolating between the learned representations. We validate our theory using numerical simulations on tasks up to 46-dimensions.

Bayesian optimization is a highly efficient approach to optimizing objective functions which are expensive to query. These objectives are typically represented by Gaussian process (GP) surrogate models which are easy to optimize and support exact inference. While standard GP surrogates have been well-established in Bayesian optimization, Bayesian neural networks (BNNs) have recently become practical function approximators, with many benefits over standard GPs such as the ability to naturally handle non-stationarity and learn representations for high-dimensional data. In this paper, we study BNNs as alternatives to standard GP surrogates for optimization. We consider a variety of approximate inference procedures for finite-width BNNs, including high-quality Hamiltonian Monte Carlo, low-cost stochastic MCMC, and heuristics such as deep ensembles. We also consider infinite-width BNNs and partially stochastic models such as deep kernel learning. We evaluate this collection of surrogate models on diverse problems with varying dimensionality, number of objectives, non-stationarity, and discrete and continuous inputs. We find: (i) the ranking of methods is highly problem dependent, suggesting the need for tailored inductive biases; (ii) HMC is the most successful approximate inference procedure for fully stochastic BNNs; (iii) full stochasticity may be unnecessary as deep kernel learning is relatively competitive; (iv) infinite-width BNNs are particularly promising, especially in high dimensions.

We consider the problem of recommending relevant content to users of an internet platform in the form of lists of items, called slates. We introduce a variational Bayesian Recurrent Neural Net recommender system that acts on time series of interactions between the internet platform and the user, and which scales to real world industrial situations. The recommender system is tested both online on real users, and on an offline dataset collected from a Norwegian web-based marketplace, FINN.no, that is made public for research. This is one of the first publicly available datasets which includes all the slates that are presented to users as well as which items (if any) in the slates were clicked on. Such a data set allows us to move beyond the common assumption that implicitly assumes that users are considering all possible items at each interaction. Instead we build our likelihood using the items that are actually in the slate, and evaluate the strengths and weaknesses of both approaches theoretically and in experiments. We also introduce a hierarchical prior for the item parameters based on group memberships. Both item parameters and user preferences are learned probabilistically. Furthermore, we combine our model with bandit strategies to ensure learning, and introduce `in-slate Thompson Sampling' which makes use of the slates to maximise explorative opportunities. We show experimentally that explorative recommender strategies perform on par or above their greedy counterparts. Even without making use of exploration to learn more effectively, click rates increase simply because of improved diversity in the recommended slates.

This paper investigates efficient deep neural networks (DNNs) to replace dense unstructured weight matrices with structured ones that possess desired properties. The challenge arises because the optimal weight matrix structure in popular neural network models is obscure in most cases and may vary from layer to layer even in the same network. Prior structured matrices proposed for efficient DNNs were mostly hand-crafted without a generalized framework to systematically learn them. To address this issue, we propose a generalized and differentiable framework to learn efficient structures of weight matrices by gradient descent. We first define a new class of structured matrices that covers a wide range of structured matrices in the literature by adjusting the structural parameters. Then, the frequency-domain differentiable parameterization scheme based on the Gaussian-Dirichlet kernel is adopted to learn the structural parameters by proximal gradient descent. On the image and language tasks, our method learns efficient DNNs with structured matrices, achieving lower complexity and/or higher performance than prior approaches that employ low-rank, block-sparse, or block-low-rank matrices.

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure, such as a low-dimensional manifold, is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. In the considered model, a usual likelihood approach can fail to estimate the target distribution consistently due to the singularity. We prove that a novel and effective solution exists by perturbing the data with an instance noise, which leads to consistent estimation of the underlying distribution with desirable convergence rates. We also characterize the class of distributions that can be efficiently estimated via deep generative models. This class is sufficiently general to contain various structured distributions such as product distributions, classically smooth distributions and distributions supported on a low-dimensional manifold. Our analysis provides some insights on how deep generative models can avoid the curse of dimensionality for nonparametric distribution estimation. We conduct a thorough simulation study and real data analysis to empirically demonstrate that the proposed data perturbation technique improves the estimation performance significantly.

Recent breakthroughs in text-to-image synthesis have been driven by diffusion models trained on billions of image-text pairs. Adapting this approach to 3D synthesis would require large-scale datasets of labeled 3D data and efficient architectures for denoising 3D data, neither of which currently exist. In this work, we circumvent these limitations by using a pretrained 2D text-to-image diffusion model to perform text-to-3D synthesis. We introduce a loss based on probability density distillation that enables the use of a 2D diffusion model as a prior for optimization of a parametric image generator. Using this loss in a DeepDream-like procedure, we optimize a randomly-initialized 3D model (a Neural Radiance Field, or NeRF) via gradient descent such that its 2D renderings from random angles achieve a low loss. The resulting 3D model of the given text can be viewed from any angle, relit by arbitrary illumination, or composited into any 3D environment. Our approach requires no 3D training data and no modifications to the image diffusion model, demonstrating the effectiveness of pretrained image diffusion models as priors.

[This paper was initially published in PHME conference in 2016, selected for further publication in International Journal of Prognostics and Health Management.] This paper describes an Autoregressive Partially-hidden Markov model (ARPHMM) for fault detection and prognostics of equipments based on sensors' data. It is a particular dynamic Bayesian network that allows to represent the dynamics of a system by means of a Hidden Markov Model (HMM) and an autoregressive (AR) process. The Markov chain assumes that the system is switching back and forth between internal states while the AR process ensures a temporal coherence on sensor measurements. A sound learning procedure of standard ARHMM based on maximum likelihood allows to iteratively estimate all parameters simultaneously. This paper suggests a modification of the learning procedure considering that one may have prior knowledge about the structure which becomes partially hidden. The integration of the prior is based on the Theory of Weighted Distributions which is compatible with the Expectation-Maximization algorithm in the sense that the convergence properties are still satisfied. We show how to apply this model to estimate the remaining useful life based on health indicators. The autoregressive parameters can indeed be used for prediction while the latent structure can be used to get information about the degradation level. The interest of the proposed method for prognostics and health assessment is demonstrated on CMAPSS datasets.

Inferring causal structures from experimentation is a central task in many domains. For example, in biology, recent advances allow us to obtain single-cell expression data under multiple interventions such as drugs or gene knockouts. However, the targets of the interventions are often uncertain or unknown and the number of observations limited. As a result, standard causal discovery methods can no longer be reliably used. To fill this gap, we propose a Bayesian framework (BaCaDI) for discovering and reasoning about the causal structure that underlies data generated under various unknown experimental or interventional conditions. BaCaDI is fully differentiable, which allows us to infer the complex joint posterior over the intervention targets and the causal structure via efficient gradient-based variational inference. In experiments on synthetic causal discovery tasks and simulated gene-expression data, BaCaDI outperforms related methods in identifying causal structures and intervention targets.

This review paper is intended for the 2nd edition of the Handbook of Markov chain Monte Carlo. We provide an introduction to approximate inference techniques as Bayesian computation methods applied to deep learning models. We organize the chapter by presenting popular computational methods for Bayesian neural networks and deep generative models, explaining their unique challenges in posterior inference as well as the solutions.

We revisit the structure learning problem for dynamic Bayesian networks and propose a method that simultaneously estimates contemporaneous (intra-slice) and time-lagged (inter-slice) relationships between variables in a time-series. Our approach is score-based, and revolves around minimizing a penalized loss subject to an acyclicity constraint. To solve this problem, we leverage a recent algebraic result characterizing the acyclicity constraint as a smooth equality constraint. The resulting algorithm, which we call DYNOTEARS, outperforms other methods on simulated data, especially in high-dimensions as the number of variables increases. We also apply this algorithm on real datasets from two different domains, finance and molecular biology, and analyze the resulting output. Compared to state-of-the-art methods for learning dynamic Bayesian networks, our method is both scalable and accurate on real data. The simple formulation and competitive performance of our method make it suitable for a variety of problems where one seeks to learn connections between variables across time.

Latent Gaussian process (GP) models are widely used in neuroscience to uncover hidden state evolutions from sequential observations, mainly in neural activity recordings. While latent GP models provide a principled and powerful solution in theory, the intractable posterior in non-conjugate settings necessitates approximate inference schemes, which may lack scalability. In this work, we propose cvHM, a general inference framework for latent GP models leveraging Hida-Mat\'ern kernels and conjugate computation variational inference (CVI). With cvHM, we are able to perform variational inference of latent neural trajectories with linear time complexity for arbitrary likelihoods. The reparameterization of stationary kernels using Hida-Mat\'ern GPs helps us connect the latent variable models that encode prior assumptions through dynamical systems to those that encode trajectory assumptions through GPs. In contrast to previous work, we use bidirectional information filtering, leading to a more concise implementation. Furthermore, we employ the Whittle approximate likelihood to achieve highly efficient hyperparameter learning.

Since a building's floorplans are easily accessible, consistent over time, and inherently robust to changes in visual appearance, self-localization within the floorplan has attracted researchers' interest. However, since floorplans are minimalist representations of a building's structure, modal and geometric differences between visual perceptions and floorplans pose challenges to this task. While existing methods cleverly utilize 2D geometric features and pose filters to achieve promising performance, they fail to address the localization errors caused by frequent visual changes and view occlusions due to variously shaped 3D objects. To tackle these issues, this paper views the 2D Floorplan Localization (FLoc) problem from a higher dimension by injecting 3D geometric priors into the visual FLoc algorithm. For the 3D geometric prior modeling, we first model geometrically aware view invariance using multi-view constraints, i.e., leveraging imaging geometric principles to provide matching constraints between multiple images that see the same points. Then, we further model the view-scene aligned geometric priors, enhancing the cross-modal geometry-color correspondences by associating the scene's surface reconstruction with the RGB frames of the sequence. Both 3D priors are modeled through self-supervised contrastive learning, thus no additional geometric or semantic annotations are required. These 3D priors summarized in extensive realistic scenes bridge the modal gap while improving localization success without increasing the computational burden on the FLoc algorithm. Sufficient comparative studies demonstrate that our method significantly outperforms state-of-the-art methods and substantially boosts the FLoc accuracy. All data and code will be released after the anonymous review.

Equivariant networks are specifically designed to ensure consistent behavior with respect to a set of input transformations, leading to higher sample efficiency and more accurate and robust predictions. However, redesigning each component of prevalent deep neural network architectures to achieve chosen equivariance is a difficult problem and can result in a computationally expensive network during both training and inference. A recently proposed alternative towards equivariance that removes the architectural constraints is to use a simple canonicalization network that transforms the input to a canonical form before feeding it to an unconstrained prediction network. We show here that this approach can effectively be used to make a large pretrained network equivariant. However, we observe that the produced canonical orientations can be misaligned with those of the training distribution, hindering performance. Using dataset-dependent priors to inform the canonicalization function, we are able to make large pretrained models equivariant while maintaining their performance. This significantly improves the robustness of these models to deterministic transformations of the data, such as rotations. We believe this equivariant adaptation of large pretrained models can help their domain-specific applications with known symmetry priors.

A fundamental question in modern machine learning is why large, over-parameterized models, such as deep neural networks and transformers, tend to generalize well, even when their number of parameters far exceeds the number of training samples. We investigate this phenomenon through the lens of information theory, grounded in universal learning theory. Specifically, we study a Bayesian mixture learner with log-loss and (almost) uniform prior over an expansive hypothesis class. Our key result shows that the learner's regret is not determined by the overall size of the hypothesis class, but rather by the cumulative probability of all models that are close, in Kullback-Leibler divergence distance, to the true data-generating process. We refer to this cumulative probability as the weight of the hypothesis. This leads to a natural notion of model simplicity: simple models are those with large weight and thus require fewer samples to generalize, while complex models have small weight and need more data. This perspective provides a rigorous and intuitive explanation for why over-parameterized models often avoid overfitting: the presence of simple hypotheses allows the posterior to concentrate on them when supported by the data. We further bridge theory and practice by recalling that stochastic gradient descent with Langevin dynamics samples from the correct posterior distribution, enabling our theoretical learner to be approximated using standard machine learning methods combined with ensemble learning. Our analysis yields non-uniform regret bounds and aligns with key practical concepts such as flat minima and model distillation. The results apply broadly across online, batch, and supervised learning settings, offering a unified and principled understanding of the generalization behavior of modern AI systems.

The posterior collapse phenomenon in variational autoencoder (VAE), where the variational posterior distribution closely matches the prior distribution, can hinder the quality of the learned latent variables. As a consequence of posterior collapse, the latent variables extracted by the encoder in VAE preserve less information from the input data and thus fail to produce meaningful representations as input to the reconstruction process in the decoder. While this phenomenon has been an actively addressed topic related to VAE performance, the theory for posterior collapse remains underdeveloped, especially beyond the standard VAE. In this work, we advance the theoretical understanding of posterior collapse to two important and prevalent yet less studied classes of VAE: conditional VAE and hierarchical VAE. Specifically, via a non-trivial theoretical analysis of linear conditional VAE and hierarchical VAE with two levels of latent, we prove that the cause of posterior collapses in these models includes the correlation between the input and output of the conditional VAE and the effect of learnable encoder variance in the hierarchical VAE. We empirically validate our theoretical findings for linear conditional and hierarchical VAE and demonstrate that these results are also predictive for non-linear cases with extensive experiments.

Existing neural rendering methods for creating human avatars typically either require dense input signals such as video or multi-view images, or leverage a learned prior from large-scale specific 3D human datasets such that reconstruction can be performed with sparse-view inputs. Most of these methods fail to achieve realistic reconstruction when only a single image is available. To enable the data-efficient creation of realistic animatable 3D humans, we propose ELICIT, a novel method for learning human-specific neural radiance fields from a single image. Inspired by the fact that humans can effortlessly estimate the body geometry and imagine full-body clothing from a single image, we leverage two priors in ELICIT: 3D geometry prior and visual semantic prior. Specifically, ELICIT utilizes the 3D body shape geometry prior from a skinned vertex-based template model (i.e., SMPL) and implements the visual clothing semantic prior with the CLIP-based pretrained models. Both priors are used to jointly guide the optimization for creating plausible content in the invisible areas. Taking advantage of the CLIP models, ELICIT can use text descriptions to generate text-conditioned unseen regions. In order to further improve visual details, we propose a segmentation-based sampling strategy that locally refines different parts of the avatar. Comprehensive evaluations on multiple popular benchmarks, including ZJU-MoCAP, Human3.6M, and DeepFashion, show that ELICIT has outperformed strong baseline methods of avatar creation when only a single image is available. The code is public for research purposes at https://huangyangyi.github.io/ELICIT/.

We introduce a deterministic variational formulation for training Bayesian last layer neural networks. This yields a sampling-free, single-pass model and loss that effectively improves uncertainty estimation. Our variational Bayesian last layer (VBLL) can be trained and evaluated with only quadratic complexity in last layer width, and is thus (nearly) computationally free to add to standard architectures. We experimentally investigate VBLLs, and show that they improve predictive accuracy, calibration, and out of distribution detection over baselines across both regression and classification. Finally, we investigate combining VBLL layers with variational Bayesian feature learning, yielding a lower variance collapsed variational inference method for Bayesian neural networks.

Prompt-based classifiers are an attractive approach for zero-shot classification. However, the precise choice of the prompt template and label words can largely influence performance, with semantically equivalent settings often showing notable performance difference. This discrepancy can be partly attributed to word biases, where the classifier may be biased towards classes. To address this problem, it is possible to optimise classification thresholds on a labelled data set, however, this mitigates some of the advantages of prompt-based classifiers. This paper instead approaches this problem by examining the expected marginal probabilities of the classes. Here, probabilities are reweighted to have a uniform prior over classes, in an unsupervised fashion. Further, we draw a theoretical connection between the class priors and the language models' word prior, and offer the ability to set a threshold in a zero-resource fashion. We show that matching class priors correlates strongly with the oracle upper bound performance and demonstrate large consistent performance gains for prompt settings over a range of NLP tasks.

We propose a structural default model for portfolio-wide valuation adjustments (xVAs) and represent it as a system of coupled backward stochastic differential equations. The framework is divided into four layers, each capturing a key component: (i) clean values, (ii) initial margin and Collateral Valuation Adjustment (ColVA), (iii) Credit/Debit Valuation Adjustments (CVA/DVA) together with Margin Valuation Adjustment (MVA), and (iv) Funding Valuation Adjustment (FVA). Because these layers depend on one another through collateral and default effects, a naive Monte Carlo approach would require deeply nested simulations, making the problem computationally intractable. To address this challenge, we use an iterative deep BSDE approach, handling each layer sequentially so that earlier outputs serve as inputs to the subsequent layers. Initial margin is computed via deep quantile regression to reflect margin requirements over the Margin Period of Risk. We also adopt a change-of-measure method that highlights rare but significant defaults of the bank or counterparty, ensuring that these events are accurately captured in the training process. We further extend Han and Long's (2020) a posteriori error analysis to BSDEs on bounded domains. Due to the random exit from the domain, we obtain an order of convergence of O(h^{1/4-epsilon}) rather than the usual O(h^{1/2}). Numerical experiments illustrate that this method drastically reduces computational demands and successfully scales to high-dimensional, non-symmetric portfolios. The results confirm its effectiveness and accuracy, offering a practical alternative to nested Monte Carlo simulations in multi-counterparty xVA analyses.

Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each task. Most inverse tasks can be formulated as inferring a posterior distribution over data (e.g., a full image) given a measurement (e.g., a masked image). This is however challenging in diffusion models since the nonlinear and iterative nature of the diffusion process renders the posterior intractable. To cope with this challenge, we propose a variational approach that by design seeks to approximate the true posterior distribution. We show that our approach naturally leads to regularization by denoising diffusion process (RED-Diff) where denoisers at different timesteps concurrently impose different structural constraints over the image. To gauge the contribution of denoisers from different timesteps, we propose a weighting mechanism based on signal-to-noise-ratio (SNR). Our approach provides a new variational perspective for solving inverse problems with diffusion models, allowing us to formulate sampling as stochastic optimization, where one can simply apply off-the-shelf solvers with lightweight iterates. Our experiments for image restoration tasks such as inpainting and superresolution demonstrate the strengths of our method compared with state-of-the-art sampling-based diffusion models.

Deep convolutional networks have become a popular tool for image generation and restoration. Generally, their excellent performance is imputed to their ability to learn realistic image priors from a large number of example images. In this paper, we show that, on the contrary, the structure of a generator network is sufficient to capture a great deal of low-level image statistics prior to any learning. In order to do so, we show that a randomly-initialized neural network can be used as a handcrafted prior with excellent results in standard inverse problems such as denoising, super-resolution, and inpainting. Furthermore, the same prior can be used to invert deep neural representations to diagnose them, and to restore images based on flash-no flash input pairs. Apart from its diverse applications, our approach highlights the inductive bias captured by standard generator network architectures. It also bridges the gap between two very popular families of image restoration methods: learning-based methods using deep convolutional networks and learning-free methods based on handcrafted image priors such as self-similarity. Code and supplementary material are available at https://dmitryulyanov.github.io/deep_image_prior .

We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical solvers. Most existing forward or inverse PDE approaches perform poorly when the observations on the data or the underlying coefficients are incomplete, which is a common assumption for real-world measurements. In this work, we propose DiffusionPDE that can simultaneously fill in the missing information and solve a PDE by modeling the joint distribution of the solution and coefficient spaces. We show that the learned generative priors lead to a versatile framework for accurately solving a wide range of PDEs under partial observation, significantly outperforming the state-of-the-art methods for both forward and inverse directions.

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex multimodal and correlated posteriors in high-dimensional spaces. Our approach introduces novel bounds for approximate inference using implicit distributions by locally linearising the neural sampler. This is distinct from existing methods that rely on additional discriminator networks and unstable adversarial objectives. Furthermore, we present a new sampler architecture that, for the first time, enables implicit distributions over tens of millions of latent variables, addressing computational concerns by using differentiable numerical approximations. We empirically show that our method is capable of recovering correlations across layers in large Bayesian neural networks, a property that is crucial for a network's performance but notoriously challenging to achieve. To the best of our knowledge, no other method has been shown to accomplish this task for such large models. Through experiments in downstream tasks, we demonstrate that our expressive posteriors outperform state-of-the-art uncertainty quantification methods, validating the effectiveness of our training algorithm and the quality of the learned implicit approximation.

Neural Posterior Estimation methods for simulation-based inference can be ill-suited for dealing with posterior distributions obtained by conditioning on multiple observations, as they tend to require a large number of simulator calls to learn accurate approximations. In contrast, Neural Likelihood Estimation methods can handle multiple observations at inference time after learning from individual observations, but they rely on standard inference methods, such as MCMC or variational inference, which come with certain performance drawbacks. We introduce a new method based on conditional score modeling that enjoys the benefits of both approaches. We model the scores of the (diffused) posterior distributions induced by individual observations, and introduce a way of combining the learned scores to approximately sample from the target posterior distribution. Our approach is sample-efficient, can naturally aggregate multiple observations at inference time, and avoids the drawbacks of standard inference methods.

In this paper, we present a novel two-stage approach that fully utilizes the information provided by the reference image to establish a customized knowledge prior for image-to-3D generation. While previous approaches primarily rely on a general diffusion prior, which struggles to yield consistent results with the reference image, we propose a subject-specific and multi-modal diffusion model. This model not only aids NeRF optimization by considering the shading mode for improved geometry but also enhances texture from the coarse results to achieve superior refinement. Both aspects contribute to faithfully aligning the 3D content with the subject. Extensive experiments showcase the superiority of our method, Customize-It-3D, outperforming previous works by a substantial margin. It produces faithful 360-degree reconstructions with impressive visual quality, making it well-suited for various applications, including text-to-3D creation.

Training data attribution (TDA) techniques find influential training data for the model's prediction on the test data of interest. They approximate the impact of down- or up-weighting a particular training sample. While conceptually useful, they are hardly applicable to deep models in practice, particularly because of their sensitivity to different model initialisation. In this paper, we introduce a Bayesian perspective on the TDA task, where the learned model is treated as a Bayesian posterior and the TDA estimates as random variables. From this novel viewpoint, we observe that the influence of an individual training sample is often overshadowed by the noise stemming from model initialisation and SGD batch composition. Based on this observation, we argue that TDA can only be reliably used for explaining deep model predictions that are consistently influenced by certain training data, independent of other noise factors. Our experiments demonstrate the rarity of such noise-independent training-test data pairs but confirm their existence. We recommend that future researchers and practitioners trust TDA estimates only in such cases. Further, we find a disagreement between ground truth and estimated TDA distributions and encourage future work to study this gap. Code is provided at https://github.com/ElisaNguyen/bayesian-tda.

It is inherently ambiguous to lift 2D results from pre-trained diffusion models to a 3D world for text-to-3D generation. 2D diffusion models solely learn view-agnostic priors and thus lack 3D knowledge during the lifting, leading to the multi-view inconsistency problem. We find that this problem primarily stems from geometric inconsistency, and avoiding misplaced geometric structures substantially mitigates the problem in the final outputs. Therefore, we improve the consistency by aligning the 2D geometric priors in diffusion models with well-defined 3D shapes during the lifting, addressing the vast majority of the problem. This is achieved by fine-tuning the 2D diffusion model to be viewpoint-aware and to produce view-specific coordinate maps of canonically oriented 3D objects. In our process, only coarse 3D information is used for aligning. This "coarse" alignment not only resolves the multi-view inconsistency in geometries but also retains the ability in 2D diffusion models to generate detailed and diversified high-quality objects unseen in the 3D datasets. Furthermore, our aligned geometric priors (AGP) are generic and can be seamlessly integrated into various state-of-the-art pipelines, obtaining high generalizability in terms of unseen shapes and visual appearance while greatly alleviating the multi-view inconsistency problem. Our method represents a new state-of-the-art performance with an 85+% consistency rate by human evaluation, while many previous methods are around 30%. Our project page is https://sweetdreamer3d.github.io/

Video representation is a long-standing problem that is crucial for various down-stream tasks, such as tracking,depth prediction,segmentation,view synthesis,and editing. However, current methods either struggle to model complex motions due to the absence of 3D structure or rely on implicit 3D representations that are ill-suited for manipulation tasks. To address these challenges, we introduce a novel explicit 3D representation-video Gaussian representation -- that embeds a video into 3D Gaussians. Our proposed representation models video appearance in a 3D canonical space using explicit Gaussians as proxies and associates each Gaussian with 3D motions for video motion. This approach offers a more intrinsic and explicit representation than layered atlas or volumetric pixel matrices. To obtain such a representation, we distill 2D priors, such as optical flow and depth, from foundation models to regularize learning in this ill-posed setting. Extensive applications demonstrate the versatility of our new video representation. It has been proven effective in numerous video processing tasks, including tracking, consistent video depth and feature refinement, motion and appearance editing, and stereoscopic video generation. Project page: https://sunyangtian.github.io/spatter_a_video_web/

We present a novel stochastic variational Gaussian process (GP) inference method, based on a posterior over a learnable set of weighted pseudo input-output points (coresets). Instead of a free-form variational family, the proposed coreset-based, variational tempered family for GPs (CVTGP) is defined in terms of the GP prior and the data-likelihood; hence, accommodating the modeling inductive biases. We derive CVTGP's lower bound for the log-marginal likelihood via marginalization of the proposed posterior over latent GP coreset variables, and show it is amenable to stochastic optimization. CVTGP reduces the learnable parameter size to O(M), enjoys numerical stability, and maintains O(M^3) time- and O(M^2) space-complexity, by leveraging a coreset-based tempered posterior that, in turn, provides sparse and explainable representations of the data. Results on simulated and real-world regression problems with Gaussian observation noise validate that CVTGP provides better evidence lower-bound estimates and predictive root mean squared error than alternative stochastic GP inference methods.

Generating images from text involving complex and novel object arrangements remains a significant challenge for current text-to-image (T2I) models. Although prior layout-based methods improve object arrangements using spatial constraints with 2D layouts, they often struggle to capture 3D positioning and sacrifice quality and coherence. In this work, we introduce ComposeAnything, a novel framework for improving compositional image generation without retraining existing T2I models. Our approach first leverages the chain-of-thought reasoning abilities of LLMs to produce 2.5D semantic layouts from text, consisting of 2D object bounding boxes enriched with depth information and detailed captions. Based on this layout, we generate a spatial and depth aware coarse composite of objects that captures the intended composition, serving as a strong and interpretable prior that replaces stochastic noise initialization in diffusion-based T2I models. This prior guides the denoising process through object prior reinforcement and spatial-controlled denoising, enabling seamless generation of compositional objects and coherent backgrounds, while allowing refinement of inaccurate priors. ComposeAnything outperforms state-of-the-art methods on the T2I-CompBench and NSR-1K benchmarks for prompts with 2D/3D spatial arrangements, high object counts, and surreal compositions. Human evaluations further demonstrate that our model generates high-quality images with compositions that faithfully reflect the text.

We introduce Motion2VecSets, a 4D diffusion model for dynamic surface reconstruction from point cloud sequences. While existing state-of-the-art methods have demonstrated success in reconstructing non-rigid objects using neural field representations, conventional feed-forward networks encounter challenges with ambiguous observations from noisy, partial, or sparse point clouds. To address these challenges, we introduce a diffusion model that explicitly learns the shape and motion distribution of non-rigid objects through an iterative denoising process of compressed latent representations. The diffusion-based priors enable more plausible and probabilistic reconstructions when handling ambiguous inputs. We parameterize 4D dynamics with latent sets instead of using global latent codes. This novel 4D representation allows us to learn local shape and deformation patterns, leading to more accurate non-linear motion capture and significantly improving generalizability to unseen motions and identities. For more temporally-coherent object tracking, we synchronously denoise deformation latent sets and exchange information across multiple frames. To avoid computational overhead, we designed an interleaved space and time attention block to alternately aggregate deformation latents along spatial and temporal domains. Extensive comparisons against state-of-the-art methods demonstrate the superiority of our Motion2VecSets in 4D reconstruction from various imperfect observations. More detailed information can be found at https://vveicao.github.io/projects/Motion2VecSets/.

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's individually, and do not leverage the dynamic distributions underlying the MTS's, leading to sub-optimal results when the sparsity is high. To address this challenge, we propose a novel generative model, which tracks the transition of latent clusters, instead of isolated feature representations, to achieve robust modeling. It is characterized by a newly designed dynamic Gaussian mixture distribution, which captures the dynamics of clustering structures, and is used for emitting timeseries. The generative model is parameterized by neural networks. A structured inference network is also designed for enabling inductive analysis. A gating mechanism is further introduced to dynamically tune the Gaussian mixture distributions. Extensive experimental results on a variety of real-life datasets demonstrate the effectiveness of our method.

We consider the general problem of recovering a high-dimensional signal from noisy quantized measurements. Quantization, especially coarse quantization such as 1-bit sign measurements, leads to severe information loss and thus a good prior knowledge of the unknown signal is helpful for accurate recovery. Motivated by the power of score-based generative models (SGM, also known as diffusion models) in capturing the rich structure of natural signals beyond simple sparsity, we propose an unsupervised data-driven approach called quantized compressed sensing with SGM (QCS-SGM), where the prior distribution is modeled by a pre-trained SGM. To perform posterior sampling, an annealed pseudo-likelihood score called noise perturbed pseudo-likelihood score is introduced and combined with the prior score of SGM. The proposed QCS-SGM applies to an arbitrary number of quantization bits. Experiments on a variety of baseline datasets demonstrate that the proposed QCS-SGM significantly outperforms existing state-of-the-art algorithms by a large margin for both in-distribution and out-of-distribution samples. Moreover, as a posterior sampling method, QCS-SGM can be easily used to obtain confidence intervals or uncertainty estimates of the reconstructed results. The code is available at https://github.com/mengxiangming/QCS-SGM.

Diffusion models have quickly risen in popularity for their ability to model complex distributions and perform effective posterior sampling. Unfortunately, the iterative nature of these generative models makes them computationally expensive and unsuitable for real-time sequential inverse problems such as ultrasound imaging. Considering the strong temporal structure across sequences of frames, we propose a novel approach that models the transition dynamics to improve the efficiency of sequential diffusion posterior sampling in conditional image synthesis. Through modeling sequence data using a video vision transformer (ViViT) transition model based on previous diffusion outputs, we can initialize the reverse diffusion trajectory at a lower noise scale, greatly reducing the number of iterations required for convergence. We demonstrate the effectiveness of our approach on a real-world dataset of high frame rate cardiac ultrasound images and show that it achieves the same performance as a full diffusion trajectory while accelerating inference 25times, enabling real-time posterior sampling. Furthermore, we show that the addition of a transition model improves the PSNR up to 8\% in cases with severe motion. Our method opens up new possibilities for real-time applications of diffusion models in imaging and other domains requiring real-time inference.

Transfer learning has recently shown significant performance across various tasks involving deep neural networks. In these transfer learning scenarios, the prior distribution for downstream data becomes crucial in Bayesian model averaging (BMA). While previous works proposed the prior over the neural network parameters centered around the pre-trained solution, such strategies have limitations when dealing with distribution shifts between upstream and downstream data. This paper introduces nonparametric transfer learning (NPTL), a flexible posterior sampling method to address the distribution shift issue within the context of nonparametric learning. The nonparametric learning (NPL) method is a recent approach that employs a nonparametric prior for posterior sampling, efficiently accounting for model misspecification scenarios, which is suitable for transfer learning scenarios that may involve the distribution shift between upstream and downstream tasks. Through extensive empirical validations, we demonstrate that our approach surpasses other baselines in BMA performance.

This paper introduces a novel hierarchical autoencoder that maps 3D models into a highly compressed latent space. The hierarchical autoencoder is specifically designed to tackle the challenges arising from large-scale datasets and generative modeling using diffusion. Different from previous approaches that only work on a regular image or volume grid, our hierarchical autoencoder operates on unordered sets of vectors. Each level of the autoencoder controls different geometric levels of detail. We show that the model can be used to represent a wide range of 3D models while faithfully representing high-resolution geometry details. The training of the new architecture takes 0.70x time and 0.58x memory compared to the baseline. We also explore how the new representation can be used for generative modeling. Specifically, we propose a cascaded diffusion framework where each stage is conditioned on the previous stage. Our design extends existing cascaded designs for image and volume grids to vector sets.

How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case. Our contributions are two-fold. First, we show that a reparameterization of the variational lower bound yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods. Second, we show that for i.i.d. datasets with continuous latent variables per datapoint, posterior inference can be made especially efficient by fitting an approximate inference model (also called a recognition model) to the intractable posterior using the proposed lower bound estimator. Theoretical advantages are reflected in experimental results.

Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit geometric properties such as equivariances. Equivariances are common in scientific models, however integrating them directly into expressive inference networks (such as normalizing flows) is not straightforward. We here describe an alternative method to incorporate equivariances under joint transformations of parameters and data. Our method -- called group equivariant neural posterior estimation (GNPE) -- is based on self-consistently standardizing the "pose" of the data while estimating the posterior over parameters. It is architecture-independent, and applies both to exact and approximate equivariances. As a real-world application, we use GNPE for amortized inference of astrophysical binary black hole systems from gravitational-wave observations. We show that GNPE achieves state-of-the-art accuracy while reducing inference times by three orders of magnitude.

This paper presents a learning-based method for transparent surface estimation from a single view polarization image. Existing shape from polarization(SfP) methods have the difficulty in estimating transparent shape since the inherent transmission interference heavily reduces the reliability of physics-based prior. To address this challenge, we propose the concept of physics-based prior, which is inspired by the characteristic that the transmission component in the polarization image has more noise than reflection. The confidence is used to determine the contribution of the interfered physics-based prior. Then, we build a network(TransSfP) with multi-branch architecture to avoid the destruction of relationships between different hierarchical inputs. To train and test our method, we construct a dataset for transparent shape from polarization with paired polarization images and ground-truth normal maps. Extensive experiments and comparisons demonstrate the superior accuracy of our method.

Maximizing the log-likelihood is a crucial aspect of learning latent variable models, and variational inference (VI) stands as the commonly adopted method. However, VI can encounter challenges in achieving a high log-likelihood when dealing with complicated posterior distributions. In response to this limitation, we introduce a novel variational importance sampling (VIS) approach that directly estimates and maximizes the log-likelihood. VIS leverages the optimal proposal distribution, achieved by minimizing the forward chi^2 divergence, to enhance log-likelihood estimation. We apply VIS to various popular latent variable models, including mixture models, variational auto-encoders, and partially observable generalized linear models. Results demonstrate that our approach consistently outperforms state-of-the-art baselines, both in terms of log-likelihood and model parameter estimation.

Linear structural equation models are multivariate statistical models encoded by mixed graphs. In particular, the set of covariance matrices for distributions belonging to a linear structural equation model for a fixed mixed graph G=(V, D,B) is parameterized by a rational function with parameters for each vertex and edge in G. This rational parametrization naturally allows for the study of these models from an algebraic and combinatorial point of view. Indeed, this point of view has led to a collection of results in the literature, mainly focusing on questions related to identifiability and determining relationships between covariances (i.e., finding polynomials in the Gaussian vanishing ideal). So far, a large proportion of these results has focused on the case when D, the directed part of the mixed graph G, is acyclic. This is due to the fact that in the acyclic case, the parametrization becomes polynomial and there is a description of the entries of the covariance matrices in terms of a finite sum. We move beyond the acyclic case and give a closed form expression for the entries of the covariance matrices in terms of the one-connections in a graph obtained from D through some small operations. This closed form expression then allows us to show that if G is simple, then the parametrization map is generically finite-to-one. Finally, having a closed form expression for the covariance matrices allows for the development of an algorithm for systematically exploring possible polynomials in the Gaussian vanishing ideal.

Bayesian neural networks (BNNs) offer uncertainty quantification but come with the downside of substantially increased training and inference costs. Sparse BNNs have been investigated for efficient inference, typically by either slowly introducing sparsity throughout the training or by post-training compression of dense BNNs. The dilemma of how to cut down massive training costs remains, particularly given the requirement to learn about the uncertainty. To solve this challenge, we introduce Sparse Subspace Variational Inference (SSVI), the first fully sparse BNN framework that maintains a consistently highly sparse Bayesian model throughout the training and inference phases. Starting from a randomly initialized low-dimensional sparse subspace, our approach alternately optimizes the sparse subspace basis selection and its associated parameters. While basis selection is characterized as a non-differentiable problem, we approximate the optimal solution with a removal-and-addition strategy, guided by novel criteria based on weight distribution statistics. Our extensive experiments show that SSVI sets new benchmarks in crafting sparse BNNs, achieving, for instance, a 10-20x compression in model size with under 3\% performance drop, and up to 20x FLOPs reduction during training compared with dense VI training. Remarkably, SSVI also demonstrates enhanced robustness to hyperparameters, reducing the need for intricate tuning in VI and occasionally even surpassing VI-trained dense BNNs on both accuracy and uncertainty metrics.

We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect Y can be written as a function of the cause X and a noise source N independent of X, which may be scaled by a positive function g over the cause, i.e., Y = f(X) + g(X)N. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of Y given X as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via either Monte Carlo or expectation-maximization methods. In this work we introduce an alternative, variational inference algorithm for Markov jump processes which relies on neural ordinary differential equations, and is trainable via back-propagation. Our methodology learns neural, continuous-time representations of the observed data, that are used to approximate the initial distribution and time-dependent transition probability rates of the posterior Markov jump process. The time-independent rates of the prior process are in contrast trained akin to generative adversarial networks. We test our approach on synthetic data sampled from ground-truth Markov jump processes, experimental switching ion channel data and molecular dynamics simulations. Source code to reproduce our experiments is available online.

Autoregressive models have achieved impressive results over a wide range of domains in terms of generation quality and downstream task performance. In the continuous domain, a key factor behind this success is the usage of quantized latent spaces (e.g., obtained via VQ-VAE autoencoders), which allow for dimensionality reduction and faster inference times. However, using existing pre-trained models to perform new non-trivial tasks is difficult since it requires additional fine-tuning or extensive training to elicit prompting. This paper introduces LASS as a way to perform vector-quantized Latent Autoregressive Source Separation (i.e., de-mixing an input signal into its constituent sources) without requiring additional gradient-based optimization or modifications of existing models. Our separation method relies on the Bayesian formulation in which the autoregressive models are the priors, and a discrete (non-parametric) likelihood function is constructed by performing frequency counts over latent sums of addend tokens. We test our method on images and audio with several sampling strategies (e.g., ancestral, beam search) showing competitive results with existing approaches in terms of separation quality while offering at the same time significant speedups in terms of inference time and scalability to higher dimensional data.

Amodal object completion is a complex task that involves predicting the invisible parts of an object based on visible segments and background information. Learning shape priors is crucial for effective amodal completion, but traditional methods often rely on two-stage processes or additional information, leading to inefficiencies and potential error accumulation. To address these shortcomings, we introduce a novel framework named the Hyper-Transformer Amodal Network (H-TAN). This framework utilizes a hyper transformer equipped with a dynamic convolution head to directly learn shape priors and accurately predict amodal masks. Specifically, H-TAN uses a dual-branch structure to extract multi-scale features from both images and masks. The multi-scale features from the image branch guide the hyper transformer in learning shape priors and in generating the weights for dynamic convolution tailored to each instance. The dynamic convolution head then uses the features from the mask branch to predict precise amodal masks. We extensively evaluate our model on three benchmark datasets: KINS, COCOA-cls, and D2SA, where H-TAN demonstrated superior performance compared to existing methods. Additional experiments validate the effectiveness and stability of the novel hyper transformer in our framework.

In bipartite networks, community structures are restricted to being disassortative, in that nodes of one type are grouped according to common patterns of connection with nodes of the other type. This makes the stochastic block model (SBM), a highly flexible generative model for networks with block structure, an intuitive choice for bipartite community detection. However, typical formulations of the SBM do not make use of the special structure of bipartite networks. Here we introduce a Bayesian nonparametric formulation of the SBM and a corresponding algorithm to efficiently find communities in bipartite networks which parsimoniously chooses the number of communities. The biSBM improves community detection results over general SBMs when data are noisy, improves the model resolution limit by a factor of 2, and expands our understanding of the complicated optimization landscape associated with community detection tasks. A direct comparison of certain terms of the prior distributions in the biSBM and a related high-resolution hierarchical SBM also reveals a counterintuitive regime of community detection problems, populated by smaller and sparser networks, where nonhierarchical models outperform their more flexible counterpart.

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.

Bayesian optimization (BO) has established itself as a leading strategy for efficiently optimizing expensive-to-evaluate functions. Existing BO methods mostly rely on Gaussian process (GP) surrogate models and are not applicable to (doubly-stochastic) Gaussian Cox processes, where the observation process is modulated by a latent intensity function modeled as a GP. In this paper, we propose a novel maximum a posteriori inference of Gaussian Cox processes. It leverages the Laplace approximation and change of kernel technique to transform the problem into a new reproducing kernel Hilbert space, where it becomes more tractable computationally. It enables us to obtain both a functional posterior of the latent intensity function and the covariance of the posterior, thus extending existing works that often focus on specific link functions or estimating the posterior mean. Using the result, we propose a BO framework based on the Gaussian Cox process model and further develop a Nystr\"om approximation for efficient computation. Extensive evaluations on various synthetic and real-world datasets demonstrate significant improvement over state-of-the-art inference solutions for Gaussian Cox processes, as well as effective BO with a wide range of acquisition functions designed through the underlying Gaussian Cox process model.

We address the task of estimating camera parameters from a set of images depicting a scene. Popular feature-based structure-from-motion (SfM) tools solve this task by incremental reconstruction: they repeat triangulation of sparse 3D points and registration of more camera views to the sparse point cloud. We re-interpret incremental structure-from-motion as an iterated application and refinement of a visual relocalizer, that is, of a method that registers new views to the current state of the reconstruction. This perspective allows us to investigate alternative visual relocalizers that are not rooted in local feature matching. We show that scene coordinate regression, a learning-based relocalization approach, allows us to build implicit, neural scene representations from unposed images. Different from other learning-based reconstruction methods, we do not require pose priors nor sequential inputs, and we optimize efficiently over thousands of images. Our method, ACE0 (ACE Zero), estimates camera poses to an accuracy comparable to feature-based SfM, as demonstrated by novel view synthesis. Project page: https://nianticlabs.github.io/acezero/

The optimization of expensive-to-evaluate black-box functions is prevalent in various scientific disciplines. Bayesian optimization is an automatic, general and sample-efficient method to solve these problems with minimal knowledge of the underlying function dynamics. However, the ability of Bayesian optimization to incorporate prior knowledge or beliefs about the function at hand in order to accelerate the optimization is limited, which reduces its appeal for knowledgeable practitioners with tight budgets. To allow domain experts to customize the optimization routine, we propose ColaBO, the first Bayesian-principled framework for incorporating prior beliefs beyond the typical kernel structure, such as the likely location of the optimizer or the optimal value. The generality of ColaBO makes it applicable across different Monte Carlo acquisition functions and types of user beliefs. We empirically demonstrate ColaBO's ability to substantially accelerate optimization when the prior information is accurate, and to retain approximately default performance when it is misleading.

Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches rely on various local heuristics for enforcing the acyclicity constraint. In this paper, we introduce a fundamentally different strategy: We formulate the structure learning problem as a purely continuous optimization problem over real matrices that avoids this combinatorial constraint entirely. This is achieved by a novel characterization of acyclicity that is not only smooth but also exact. The resulting problem can be efficiently solved by standard numerical algorithms, which also makes implementation effortless. The proposed method outperforms existing ones, without imposing any structural assumptions on the graph such as bounded treewidth or in-degree. Code implementing the proposed algorithm is open-source and publicly available at https://github.com/xunzheng/notears.

We present a method for generating consistent novel views from a single source image. Our approach focuses on maximizing the reuse of visible pixels from the source image. To achieve this, we use a monocular depth estimator that transfers visible pixels from the source view to the target view. Starting from a pre-trained 2D inpainting diffusion model, we train our method on the large-scale Objaverse dataset to learn 3D object priors. While training we use a novel masking mechanism based on epipolar lines to further improve the quality of our approach. This allows our framework to perform zero-shot novel view synthesis on a variety of objects. We evaluate the zero-shot abilities of our framework on three challenging datasets: Google Scanned Objects, Ray Traced Multiview, and Common Objects in 3D. See our webpage for more details: https://yashkant.github.io/invs/

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or whether a patient has died or not), because the ground-truth probabilities of the events of interest are typically unknown. The problem is therefore analogous to binary classification, with the difference that the objective is to estimate probabilities rather than predicting the specific outcome. This work investigates probability estimation from high-dimensional data using deep neural networks. There exist several methods to improve the probabilities generated by these models but they mostly focus on model (epistemic) uncertainty. For problems with inherent uncertainty, it is challenging to evaluate performance without access to ground-truth probabilities. To address this, we build a synthetic dataset to study and compare different computable metrics. We evaluate existing methods on the synthetic data as well as on three real-world probability estimation tasks, all of which involve inherent uncertainty: precipitation forecasting from radar images, predicting cancer patient survival from histopathology images, and predicting car crashes from dashcam videos. We also give a theoretical analysis of a model for high-dimensional probability estimation which reproduces several of the phenomena evinced in our experiments. Finally, we propose a new method for probability estimation using neural networks, which modifies the training process to promote output probabilities that are consistent with empirical probabilities computed from the data. The method outperforms existing approaches on most metrics on the simulated as well as real-world data.