# RecDiff: Diffusion Model for Social Recommendation

Zongwei Li  University of Hong KongHong KongChina<EMAIL_ADDRESS>,
Lianghao Xia  University of Hong KongHong KongChina<EMAIL_ADDRESS>and
Chao Huang  University of Hong KongHong KongChina<EMAIL_ADDRESS>
###### Abstract.

Social recommendation has emerged as a powerful approach to enhance
personalized recommendations by leveraging the social connections among users,
such as following and friend relations observed in online social platforms.
The fundamental assumption of social recommendation is that socially-connected
users exhibit homophily in their preference patterns. This means that users
connected by social ties tend to have similar tastes in user-item activities,
such as rating and purchasing. However, this assumption is not always valid
due to the presence of irrelevant and false social ties, which can contaminate
user embeddings and adversely affect recommendation accuracy. To address this
challenge, we propose a novel diffusion-based social denoising framework for
recommendation (RecDiff). Our approach utilizes a simple yet effective hidden-
space diffusion paradigm to alleivate the noisy effect in the compressed and
dense representation space. By performing multi-step noise diffusion and
removal, RecDiff possesses a robust ability to identify and eliminate noise
from the encoded user representations, even when the noise levels vary. The
diffusion module is optimized in a downstream task-aware manner, thereby
maximizing its ability to enhance the recommendation process. We conducted
extensive experiments to evaluate the efficacy of our framework, and the
results demonstrate its superiority in terms of recommendation accuracy,
training efficiency, and denoising effectiveness. The source code for the
model implementation is publicly available at:
https://github.com/HKUDS/RecDiff.

††copyright: none

##  1\. Introduction

Personalized recommender systems are pivotal in inferring users’ preferences
for items and are extensively utilized in various online services, including
e-commerce systems (e.g., Alibaba and Amazon) (zhang2019deep, ;
yeh2023planning, ) and content sharing platforms (e.g., Tiktok and Netflix)
(liu2021concept, ). To overcome the challenge posed by limited user-item
interactions, recent research has incorporated social relation data among
users as an additional source of information. Known as social recommendation,
these approaches aim to uncover shared preference patterns among socially-
connected users, thereby enhancing user representations and improving
recommendation performance (du2022socially, ).

Various social recommendation models have emerged, utilizing different
technologies such as matrix factorization (yang2016social, ), attention
mechanism (chen2019social, ), and graph neural network (wu2019neural, ). These
models encode user-item interactions and user-wise social connections in a
latent space, collaboratively fusing representations to enhance preference
modeling. Recent studies, including SAMN (chen2019social, ) and EATNN
(chen2019efficient, ), incorporate attention mechanisms for capturing user
relationships through weighted aggregation. Additionally, graph neural
networks have also gained attention, with proposed encoders like DiffNet
(wu2019neural, ), DGRec (song2019session, ), GraphRec (fan2019graph, ), and
DANSER (wu2019dual, ) emphasizing the extraction of high-order social
connectivities.

Despite significant progress in social recommendation, a persistent challenge
is the presence of inherent noise in social information. While auxiliary
social data captures user relationships reflecting shared interests, it can
also include irrelevant or false social connections that contradict users’
similarity in preferences. Real-world social networks often have social links
such as acquaintances and colleagues, which are unrelated to shared interests,
resulting in socially-connected users exhibiting diverse preference patterns.
This noisy social information can misguide recommenders by overemphasizing
similarities between socially-connected users with limited shared interests.
State-of-the-art GNN-based methods are particularly susceptible to this
misleading effect due to their information propagation process on noisy social
edges.

While there are limited works that attempt to address denoising social
information for recommendation, handcrafted self-supervised learning
techniques may offer limited help in reducing ambiguity in social links. For
instance, MHCN (yu2021self, ) and KCGN (huang2021knowledge, ) utilize local-
global mutual information maximization to constrain the extracted semantics of
specific social edges using social community features at the subgraph level.
SDCRec (du2022socially, ) and DcRec (wu2022disentangled, ) employ self-
discrimination tasks, leveraging the contrastive learning paradigm for social
recommenders. However, their pre-defined self-supervised learning (SSL) tasks
may not effectively align with the objective of denoising social
recommendation in two aspects.

(i) These approaches heavily depend on handcrafted targets that may contain
noise. In particular, the local-global infomax paradigm assumes less noise in
global information, but the global social context can undergo semantic shifts.
Contrastive learning introduces noise through random permutations.

(ii) These self-supervised learning tasks fail to consider the wide array of
social noise types and intensities. Infomax and contrastive approaches solely
concentrate on specific deviations in social-aware user preferences without
distinguishing between varying levels of noisy social dependencies. For
instance, users with different social behaviors may exhibit varying degrees of
irrelevant or false social links when it comes to modeling similar interests.

Based on the above discussions, two fundamental questions arise regarding our
social information denoiser for recommendation:

  * •

How can we design suitable training targets that directly align with the
denoising task for social recommendation?

  * •

How can we effectively capture social dependencies in user preferences while
accounting for varying levels of noisy connections?

To address the aforementioned challenges, we present a social diffusion model,
called RecDiff, which combines the distinguishing capabilities of generative
diffusion models with effective denoising-based training objectives. Our
RecDiff model excels in capturing data distributions and filtering noise in
social graph structures, enabling accurate modeling of user similarities based
on their preferences. Additionally, we employ a refined noise diffusion and
removal process, allowing our social recommender to effectively handle various
types of connection noise.

Our RecDiff addresses the challenge of eliminating noisy social information by
leveraging a diffusion model within a joint modeling framework that
encompasses social relationships among users and interaction between users and
items. To begin, RecDiff encodes the structural features from both the social
and interaction graphs into low-dimensional embeddings. These embeddings serve
as the foundation for subsequent refinement through our diffusion-based
denoiser. The denoiser is trained using a multi-step noise diffusion and
elimination process within the representation space. By sampling different
diffusion steps, our approach gains exposure to a wide range of noise scales,
enhancing its ability to handle various types of social noise. Compared to
diffusion models operating directly on the original graph domain, our hidden-
space diffusion paradigm exhibits higher efficiency and a more compact
solution space. Finally, the revised social embeddings are merged with user-
item interaction modeling, resulting in improved recommendations that
incorporate denoised social information.

The key contributions of this paper are summarized as follows:

  * •

We present the RecDiff framework, a novel approach that enhances social
recommender systems by effectively denoising social connections among users
with a diffusion model.

  * •

Within our RecDiff framework, we introduce an effective and efficient hidden-
space diffusion paradigm. Through multi-step noise propagation and removal
training, our model acquires robust denoising capabilities, enabling it to
effectively handle diverse social connections among users. As a result, our
model produces accurate user preference representations.

  * •

We conduct a comprehensive empirical study of our RecDiff framework,
demonstrating its superiority in terms of recommendation performance and
denoising capability.

##  2\. Preliminaries

###  2.1. Social-aware Collaborative Graph

We denote the users as $\mathcal{U}=\\{u\\}$ and the items as
$\mathcal{V}=\\{v\\}$. The user-item interactions are represented by
$\textbf{R}\in\mathbb{R}^{|\mathcal{U}|\times|\mathcal{V}|}$, while the user-
user social relations are represented by
$\textbf{S}\in\mathbb{R}^{|\mathcal{U}|\times|\mathcal{U}|}$. The user-item
interactions capture historical user behaviors on items, e.g., clicks and
views. Each element $r_{u,v}\in\textbf{R}$ is set as 1 if an interaction is
observed between user $u$ and item $v$, and $r_{u,v}=0$ otherwise. Similarly,
the social relation between a pair of users $(u,u^{\prime})$ is represented by
the binary element $s_{u,u^{\prime}}\in\textbf{S}$. Here, $s_{u,u^{\prime}}=1$
denotes social connections like friendship or following, while
$s_{u,u^{\prime}}=0$ indicates no such observation between user $u$ and
$u^{\prime}$.

To capture high-order connections in user-item interactions and user-user
social relations, we transform them into graph-structured forms. The
collaborative graph for user-item interactions, denoted as
$\mathcal{G}_{r}=(\mathcal{U},\mathcal{V},\mathcal{E}_{r})$, represents the
relationships between users and items, where
$\mathcal{E}_{r}={(u,v)|r_{u,v}=1}$ represents the edge set. Similarly, the
social graph based on user connections, denoted as
$\mathcal{G}_{s}=(\mathcal{U},\mathcal{E}_{s})$, captures the social relations
between users, with $\mathcal{E}_{s}={(u,u^{\prime})|s_{u,u^{\prime}}=1}$
representing the edge set.

###  2.2. Graph-based Social Recommender

State-of-the-art social recommendation methods typically utilize GNN-based
encoding functions on collaborative graphs and social graphs to learn
representations for users and items. These representations capture preference
patterns and enable accurate prediction of user-item interactions. The
paradigm can be formulated as:

(1)
$\displaystyle\hat{r}_{u,v}=\textbf{Pred}(\textbf{e}_{u},\textbf{e}_{v}),\leavevmode\nobreak\
\textbf{E}=\textbf{Agg}(\textbf{E}^{r},\textbf{E}^{s}),\leavevmode\nobreak\
\textbf{E}^{*}=\textbf{Enc}(\mathcal{G}_{*})$

where $\textbf{E}^{*}$ denotes $\textbf{E}^{r}$ or $\textbf{E}^{s}$ and
$\mathcal{G}_{*}$ denotes $\mathcal{G}_{r}$ or $\mathcal{G}_{s}$ for
simplicity. The collaborative graph $\mathcal{G}_{r}$ and the social graph
$\mathcal{G}_{s}$ are firstly encoded by the GNN-based encoding function
$\textbf{Enc}(\cdot)$ to produce node representations
$\textbf{E}^{r}\in\mathbb{R}^{(|\mathcal{U}|+|\mathcal{V}|)\times d}$ and
$\textbf{E}^{s}\in\mathbb{R}^{|\mathcal{U}|\times d}$, respectively. The dual-
view embeddings are then aggregated by a pooling method $\textbf{Agg}(\cdot)$
to yield the final node embeddings
$\textbf{E}\in\mathbb{R}^{(|\mathcal{U}|+|\mathcal{V}|)\times d}$. The
embeddings are finally used by a predicting function $\textbf{Pred}(\cdot)$,
such as the dot-product operation, to output predictions $\hat{r}_{u,v}$ for
user-item interactions.

##  3\. Methodology

Figure 1. Overall architecture of the proposed RecDiff framework.

###  3.1. Graph-based Collaborative Pattern Encoder

Taking inspiration from the success of simplified Graph Neural Networks (GNNs)
(he2020lightgcn, ), we utilize a lightweight Graph Convolutional Network (GCN)
as the graph encoder in our social denoising framework. This encoder operates
on the user-item interaction graph $\mathcal{G}_{r}$ and follows an iterative
message passing process described as:

(2)
$\displaystyle\textbf{E}^{r}=\sum_{l=0}^{L}\textbf{E}^{r}_{l},\leavevmode\nobreak\
\leavevmode\nobreak\
\textbf{E}^{r}_{l}={h}(\textbf{D}^{-1/2}\textbf{A}^{r}\textbf{D}^{-1/2}\textbf{E}^{r}_{l-1}\textbf{W})$

Here,
$\textbf{A}^{r}\in\mathbb{R}^{(|\mathcal{U}|+|\mathcal{V}|)\times(|\mathcal{U}|+|\mathcal{V}|)}$
denotes the adjacency matrix of the collaborative graph $\mathcal{G}_{r}$, and
D is the corresponding diagonal degree matrix. The embedding matrix
$\textbf{E}^{r}_{l}\in\mathbb{R}^{(|\mathcal{U}|+|\mathcal{V}|)\times d}$
captures the embeddings in the $l$-th iteration of the GCN. The initial
embeddings, $\textbf{E}^{r}_{0}$, are randomly generated learnable parameters.
In each iteration, the current embeddings are propagated to their neighboring
nodes using the Laplacian-normalized adjacency matrix, and the $l_{2}$
embedding normalization function $h(\cdot)$ is applied. After $L$ iterations,
the final user and item embeddings, $\textbf{E}^{r}$, are obtained by element-
wise summation of the multi-order node embeddings.

###  3.2. Diffusion-based Social Relation Denoising

####  3.2.1. Hidden-Space Social Diffusion

Drawing inspiration from the success of diffusion models in generating noise-
free data across various domains, such as images (saharia2022palette, ) and
text (li2022diffusion, ), our RecDiff framework introduces a diffusion model
to generate denoised social relation data. Considering the inherent sparsity
of social graph data, we propose an approach that enables efficient and
effective social diffusion by conducting forward and reverse diffusion
processes in the latent space, rather than the graph data space. Figure 2
provides an illustration of this hidden-space social diffusion mechanism, and
its process can be summarized by the following formula:

(3)
$\displaystyle\mathcal{G}_{s}\stackrel{{\scriptstyle\phi}}{{\longrightarrow}}\textbf{E}^{s}\stackrel{{\scriptstyle\psi}}{{\longrightarrow}}\tilde{\textbf{E}}^{s}\stackrel{{\scriptstyle\psi^{\prime}}}{{\longrightarrow}}\hat{\textbf{E}}^{s}\stackrel{{\scriptstyle\phi^{\prime}}}{{\longrightarrow}}\hat{\mathcal{G}}_{s}$

Here, $\phi$ and $\phi^{\prime}$ represent bidirectional projections between
the graph data domain and the hidden embedding domain. $\psi$ and
$\psi^{\prime}$ refer to the forward and reverse processes of the diffusion
model, where $\psi$ introduces noise to $\textbf{E}^{s}$, and $\psi^{\prime}$
is optimized to remove this noise in the hidden space.

In graph-based recommendation, the encoding function $\textbf{Enc}(\cdot)$ and
the predictive function $\textbf{Pred}(\cdot)$ are crucial for accurately
compressing and reconstructing graph structures. By regarding them as the
aforementioned projections $\phi$ and $\phi^{\prime}$, respectively, these
paired projections become invertible to each other. This property implies that
by learning the hidden-space denoiser $\psi^{\prime}$, our hidden-space
diffusion model can effectively filter out noise present in the graph-
structured data $\mathcal{G}$. Furthermore, due to the low-dimensional nature
of the hidden space, training the hidden-space denoiser $\psi^{\prime}$ is
significantly easier compared to directly denoising in the graph data space.
Building on the aforementioned considerations, we utilize a similar GCN model
as the learnable $\phi$ projection, following the formulation in Eq 2.
Subsequently, we design our social denoiser based on the acquired embeddings
$\textbf{E}^{s}\in\mathbb{R}^{|\mathcal{U}|\times d}$.

####  3.2.2. Forward and Reverse Diffusion

Based on the social relation data $\textbf{E}^{s}$ in the latent embedding
space, we design the forward and reverse processes for our hidden-space
diffusion. In the forward process, Gaussian noise is incrementally added to
the original data $\textbf{E}^{s}$ until it eventually transforms into
complete Gaussian noise. Conversely, the backward process utilizes trainable
neural networks to eliminate noise, enabling the generation of noise-less
social data.

Forward Process. In the forward process, our RecDiff iteratively applies $T$
noise steps, where $T$ is a hyperparameter. The data at the $t$-th step is
denoted as $\textbf{E}_{t}$ (omitting the superscript $s$ for simplicity), and
the 0-step data is the original data, i.e., $\textbf{E}_{0}=\textbf{E}^{s}$.
The $t$-step data is calculated from the $(t-1)$-step data as follows:

(4) $\displaystyle
q(\textbf{E}_{t}|\textbf{E}_{t-1})=\mathcal{N}(\textbf{E}_{t};\sqrt{1-\beta_{t}}\textbf{E}_{t-1},\beta_{t}\textbf{I})$

Here, $\mathcal{N}$ represents the Gaussian distribution. The parameter
$\beta_{t}$ controls the magnitude of the noise. It has been shown that by
gradually increasing $\beta_{t}$ for $t=1,\cdots,T$, the noised data
$\textbf{E}_{t}$ converges to complete Gaussian noise as $t$ increases
(ho2020denoising, ). This property allows our noise diffusion process to cover
a wide range of noise levels in the data. To generate $\beta_{t}$, we use a
linear interpolation sequence $s$ between two hyperparameters $\bar{s}{max}$
and $\bar{s}{min}$:

(5) $\displaystyle\beta_{t}=1-s_{t}/s_{t-1},\leavevmode\nobreak\
\leavevmode\nobreak\ s=(1,\bar{s}_{max},\cdots,\bar{s}_{min})$

Due to the additivity property of Gaussian distributions, the $t$-step data
can be directly calculated using only $\textbf{E}_{0}$ and pre-computed values
related to the $\beta_{t}$ sequence. This significantly speeds up the forward
process by avoiding iterative calculations. Let $\alpha_{t}=1-\beta_{t}$ and
$\bar{\alpha}t=\prod{t^{\prime}=1}^{T}\alpha_{t^{\prime}}$, the iterative
formulation of $\textbf{E}_{t}$ can be simplified to an equation that depends
only on $\textbf{E}_{0}$ and $\bar{\alpha}_{t}$:

$\displaystyle\textbf{E}_{t}$
$\displaystyle=\sqrt{\alpha_{t}}\textbf{E}_{t-1}+\sqrt{\beta_{t}}\textbf{N}_{1}$
$\displaystyle=\sqrt{\alpha_{t}}(\sqrt{\alpha_{t-1}}\textbf{E}_{t-2}+\sqrt{\beta_{t-1}}\textbf{N}_{2})+\sqrt{\beta_{t}}\textbf{N}_{1}$
$\displaystyle=\sqrt{\alpha_{t}\alpha_{t-1}}\textbf{E}_{t-2}+\sqrt{1-\alpha_{t}\alpha_{t-1}}\textbf{N}^{\prime}_{2}$
(6)
$\displaystyle=\sqrt{\bar{\alpha}_{t}}\textbf{E}_{0}+\sqrt{1-\bar{\alpha}_{t}}{\textbf{N}}^{\prime}_{t}$

Here, N, $\textbf{N}^{\prime}$ denote independent Gaussian distributions
following $\mathcal{N}(0,\textbf{I})$. Due to the addition rule of Gaussian
distributions, the term
$\sqrt{\alpha_{t}-\alpha_{t}\alpha_{t-1}}\textbf{N}_{2}+\sqrt{1-\alpha_{t}}\textbf{N}_{1}$
follows $\mathcal{N}(0,\sqrt{1-\alpha_{t}\alpha_{t-1}})$. By pre-calculating
$\bar{\alpha}_{t}$ for $1\leq t\leq T$, $\textbf{E}_{t}$ can be efficiently
obtained without recursion, facilitating random sampling for the diffusion
step $t$.

Reverse Process. In the reverse process, our objective is to restore the
social relation data in the hidden space from the noisy data $\textbf{E}_{t}$,
where $t=1,\cdots,T$. Specifically, this process aims to estimate the
following conditional probability using learnable neural networks:

(7) $\displaystyle
p(\textbf{E}_{t-1}|\textbf{E}_{t})=\mathcal{N}\left(\textbf{E}_{t-1};\mathbf{\mu}_{\theta}(\textbf{E}_{t},t),\mathbf{\Sigma}_{\theta}(\textbf{E}_{t},t)\right)$

Here, $\mathbf{\mu}_{\theta}(\cdot)$ and $\mathbf{\Sigma}_{\theta}(\cdot)$
represent neural networks with learnable parameters $\theta$ used to estimate
the Gaussian distribution. We concatenate the $t$-step data vector with a time
step-specific embedding as the input. The network consists of two fully-
connected layers:

(8)
$\displaystyle\mathbf{\mu}_{\theta}(\textbf{e}_{t},t)=\textbf{FC}^{2}(\textbf{e}_{t}\|\textbf{h}_{t}),\leavevmode\nobreak\
\leavevmode\nobreak\
\textbf{FC}(\textbf{x})=\delta(\textbf{W}\textbf{x}+\textbf{b})$

In the above equations, $\textbf{FC}^{2}(\cdot)$ represents two consecutive
fully-connected layers. $\textbf{e}_{t}\in\mathbb{R}^{d}$ denotes a node
embedding vector in the $t$-th diffusion step, and
$\textbf{h}_{t}\in\mathbb{R}^{d^{\prime}}$ represents the embedding for the
$t$-th time step. $\delta(\cdot)$, W, and b refer to the activation function,
linear transformation, and bias vectors for the fully-connected layer.

####  3.2.3. Diffusion Loss Function

The learnable denoising process of our hidden-space social diffusion is
optimized by maximizing the evidence lower bound (ELBO) of the input social
embeddings $\textbf{E}_{0}$. This ELBO term can be decomposed as follows:

$\displaystyle\log p(\textbf{e}_{0})=\log\int
p\left(\textbf{e}_{0:T}\right)\mathrm{d}\textbf{e}_{1:T}=\log\mathbb{E}_{q(\textbf{e}_{1:T}|\textbf{e}_{0})}\frac{p(\textbf{e}_{0:T})}{q(\textbf{e}_{1:T}|\textbf{e}_{0})}$
$\displaystyle\geq\underbrace{\mathbb{E}_{q\left(\textbf{e}_{1}|\textbf{e}_{0}\right)}\left[\log
p_{\theta}\left(\textbf{e}_{0}|\textbf{e}_{1}\right)\right]}_{(\text{reconstruction
term)
}}-\underbrace{D_{\mathrm{KL}}\left(q\left(\textbf{e}_{T}|\textbf{e}_{0}\right)\|p\left(\textbf{e}_{T}\right)\right)}_{\text{(prior
matching term) }}$ (9)
$\displaystyle-\sum_{t=2}^{T}\underbrace{\mathbb{E}_{q\left(\textbf{e}_{t}|\textbf{e}_{0}\right)}\left[D_{\mathrm{KL}}\left(q\left(\textbf{e}_{t-1}|\textbf{e}_{t},\textbf{e}_{0}\right)\|p_{\theta}\left(\textbf{e}_{t-1}|\textbf{e}_{t}\right)\right)\right]}_{\text{(denoising
matching term) }}$

Since the prior matching term is a constant, it can be omitted in the loss
function for optimization. The denoising matching term aims to minimize the KL
divergence between the true distribution
$q(\textbf{e}_{t-1}|\textbf{e}_{t},\textbf{e}_{0})$ and our denoiser
$p_{\theta}(\textbf{e}_{t-1}|\textbf{e}_{t})$. Following previous works (Ho et
al., 2020; Wang et al., 2023), we simplify the learning process by omitting
the learning of the standard deviation network and assume that
$\mathbf{\Sigma}_{\theta}(\textbf{e}_{t},t)=\sigma^{2}(t)\textbf{I}$. The
denoising matching term for the $t$-th time step can be defined as follows:

$\displaystyle\mathcal{L}_{t}$
$\displaystyle=\mathbb{E}_{q\left(\textbf{e}_{t}|\textbf{e}_{0}\right)}\left[D_{\mathrm{KL}}\left(q\left(\textbf{e}_{t-1}|\textbf{e}_{t},\textbf{e}_{0}\right)\|p_{\theta}\left(\textbf{e}_{t-1}|\textbf{e}_{t}\right)\right)\right]$
(10)
$\displaystyle=\mathbb{E}_{q(\textbf{e}_{t}|\textbf{e}_{0})}\left[\frac{1}{2\sigma^{2}(t)}\left[\|\mathbf{\mu}_{\theta}(\textbf{e}_{t},t)-\mathbf{\mu}(\textbf{e}_{t},\textbf{e}_{0},t)\|_{2}^{2}\right]\right]$

$\mathbf{\mu}\theta(\textbf{e}_{t},t)$ represents the output of our mean value
predictor for an embedding vector $\textbf{e}_{t}$, and
$\mathbf{\mu}(\textbf{e}_{t},\textbf{e}_{0},t)$ denotes the mean value for the
true probability. These mean value terms can be decomposed into components
related to $\textbf{e}_{t}$, $\textbf{e}_{0}$, and the output of a prediction
network $\hat{\textbf{e}}\theta(\textbf{e}_{t},t)$ for the real data
$\textbf{e}_{0}$. As a result, $\mathcal{L}_{t}$ can be expressed as:

(11)
$\displaystyle\mathcal{L}_{t}=\mathbb{E}_{q(\textbf{e}_{t}|\textbf{e}_{0})}\left[\frac{1}{2}\left(\frac{\bar{\alpha}_{t-1}}{1-\bar{\alpha}_{t-1}}-\frac{\bar{\alpha}_{t}}{1-\bar{\alpha}_{t}}\right)\|\hat{\textbf{e}}_{\theta}(\textbf{e}_{t},t)-\textbf{e}_{0}\|_{2}^{2}\right]$

The reconstruction term can be represented as the squared loss between the
predicted value $\hat{\textbf{e}}\theta(\textbf{e}_{1},1)$ and the real
embedding vector $\textbf{e}_{0}$. This term is denoted as
$\mathcal{L}^{{}^{\prime}}_{t}$ and defined as follows:

(12)
$\displaystyle\mathcal{L}^{{}^{\prime}}_{t}=\mathbb{E}_{q(\textbf{e}_{t}|\textbf{e}_{0})}\left[\|\hat{\textbf{e}}_{\theta}(\textbf{e}_{1},1)-\textbf{e}_{0}\|_{2}^{2}\right]$

Figure 2. Illustration for the hidden-space social diffusion.

####  3.2.4. Inference Process

During the inference process, we focus on removing noise from the observed
social data and utilize the denoised embeddings for making predictions. The
social denoiser takes the encoded social embeddings $\textbf{E}^{s}$ as input,
skipping the forward noise diffusion process. In the denoising step, we
iteratively remove noise by updating
$\hat{\textbf{e}}_{t-1}=\hat{{\mu}}_{\theta}(\hat{\textbf{e}}_{t},t)$, where
$\hat{{\mu}}_{\theta}(\hat{\textbf{e}}_{t},t)$ is defined as follows:

(13)
$\displaystyle\hat{{\mu}}_{\theta}\left(\hat{\textbf{e}}_{t},t\right)=\frac{\sqrt{\alpha_{t}\left(1-\bar{\alpha}_{t-1}\right)}}{1-\bar{\alpha}_{t}}\hat{\textbf{e}}_{t}+\frac{\sqrt{\bar{\alpha}_{t-1}\left(1-\alpha_{t}\right)}}{1-\bar{\alpha}_{t}}\hat{\textbf{e}}_{\theta}\left(\hat{\textbf{e}}_{t},t\right)$

We predict $\hat{\textbf{e}}_{0}$ based on $\hat{\textbf{e}}{t}$ and $t$,
denoted as $\hat{\textbf{e}}_{\theta}$. We then use the derived
$\hat{\textbf{e}}{0}$ for consecutive predictions. The inference procedure is
outlined in Algorithm 1.

Input: The social tie embedding $\textbf{E}^{S}$.

Output: the denoising embedding $\hat{\textbf{e}}_{0}$.

1 Set $\hat{\textbf{E}_{t}}$ = $\hat{\textbf{E}_{0}}$;

2 for  _t = $T$,…,1 _ do

3
$\hat{\textbf{e}}_{t-1}=\hat{\bm{\mu}}_{\theta}\left(\hat{\textbf{e}}_{t},t\right)$
obtained from $\hat{\textbf{e}}_{t}$ and $\hat{\textbf{e}}_{\theta}(.)$ via Eq
13;

4 end for

5 return the denoising $\hat{\textbf{e}}_{0}$;

Algorithm 1 Inference of our RecDiff framework.

###  3.3. Prediction and Optimization

Using the hidden-space social diffusion module, we combine the denoised social
relation with the encoded interaction patterns to obtain final embeddings for
predictions. This is done as follows:

(14)
$\displaystyle\hat{r}_{u,v}=\tilde{\textbf{e}}_{u}^{\top}\textbf{e}_{v}^{r},\leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\
\tilde{\textbf{e}}_{u}=\textbf{e}_{u}^{r}+\hat{\textbf{e}}_{\theta}(\textbf{e}_{u,t},t)$

where $t$ represents a sampled diffusion step for user $u$. We optimize our
RecDiff using the predictions $\hat{r}_{u,v}$ and a combination of
recommendation loss and diffusion loss functions:

(15)
$\displaystyle\mathcal{L}=\sum_{u,v^{+},v^{-}}-\log\sigma(\hat{r}_{u,v^{+}}-\hat{r}_{u,v^{-}})+\lambda_{1}\sum_{t}\mathcal{L}^{\prime}_{t}$

$(u,v^{+},v^{-})$ is a triplet sample for pairwise recommendation training
(rendle2009bpr, ). The diffusion loss is calculated on sampled diffusion steps
$t$ for embeddings. We also apply weight-decay regularization, with weight
$\lambda_{2}$, to all trainable parameters $\mathbf{\mathbf{\Theta}}$. The
learning process of RecDiff, including graph encoding, multi-step forward and
back diffusion, and loss calculations.

###  3.4. Model Complexity Analysis

This section provides a comprehensive analysis of the time and space
complexity of our RecDiff with the social diffusion module.

Time Complexity: Initially, RecDiff performs graph-level information
propagation on both the holistic collaborative graph $\mathcal{G}_{r}$ and the
social graph $\mathcal{G}_{s}$. This process requires
$\mathcal{O}((|\mathcal{E}_{r}|+|\mathcal{E}_{s}|)\times d)$ calculations for
message passing and $\mathcal{O}((|\mathcal{U}|+|\mathcal{V}|)\times d^{2})$
for embedding transformation. However, our social diffusion model operates
exclusively on the current batch during each training step. Let $B$ be the
number of user-item interaction pairs in each batch. The forward diffusion
process costs $\mathcal{O}(B\times d)$ computations, while the reverse process
costs $\mathcal{O}(B\times(d^{2}+dd^{\prime}))$. Theoretical analysis suggests
that our RecDiff achieves comparable time costs to common social
recommendation methods based on GNNs.

Memory Complexity: The graph encoding process of our RecDiff model requires a
similar number of parameters as conventional graph-based social recommenders.
The hidden-space diffusion network employs $\mathcal{O}(d^{2}+dd^{\prime})$
parameters for the denoiser. In comparison, diffusion models operating on the
original graph data typically require $\mathcal{O}(|\mathcal{U}|\times d)$
parameters for the trained denoising process. This distinction results in the
denoiser of our RecDiff having a smaller solution space, thereby alleviating
optimization challenges.

##  4\. Evaluation

In this section, we analyze the performance of our RecDiff framework by
exploring the following research questions (RQs):

  * •

RQ1: How does the performance of our RecDiff model compare to various
recommendation baseline methods?

  * •

RQ2: What are the effects of different designed modules in our RecDiff
framework on recommendation performance?

  * •

RQ3: How do different settings of key hyperparameters impact the
recommendation accuracy of our RecDiff method?

  * •

RQ4: What impact does the noise scale in the noise diffusion process of our
RecDiff have on the model’s performance?

  * •

RQ5: How does the efficiency of RecDiff compare to baselines?

  * •

RQ6: How effectively can our RecDiff with the social diffusion model handle
noisy user connections?

  * •

RQ7: Can our social relation denoiser provide explainability?

Table 1. Statistics of experimental datasets. Dataset | Ciao | Yelp | Epinions
---|---|---|---
# of Users | 1925 | 99262 | 14680
# of Items | 15053 | 105142 | 233261
# of User-Item Interactions | 23223 | 672513 | 447312
# of Social Interactions | 65084 | 1298522 | 632144

###  4.1. Experimental Settings

####  4.1.1. Experimental Datasets

We conducted experiments on three publicly available datasets from real-world
commercial platforms: Yelp, Ciao, and Epinions. The user-item interaction data
was based on users’ review records, where an interaction $(u,v)$ exists if
user $u$ reviewed item $v$. For user-wise social relationships, we established
connections between users $(u,u^{\prime})$ if user $u^{\prime}$ is in the
trust list of user $u$. Table 1 presents the statistics of these datasets.
Here is a summary of the dataset information:

  * •

Yelp: This data originates from Yelp and records user feedback on venues. It
includes social relationships between users, emphasizing networks formed by
individuals with shared interests.

  * •

Ciao: The Ciao dataset is sourced from the Ciao platform and captures user
reviews and ratings across a wide range of products and services. It provides
detailed information on social interactions among users, highlighting networks
formed through shared preferences and engagements.

  * •

Epinions: This data collects user feedback on various items from the social
network-based review platform Epinions (fan2019graph, ). It categorizes
ratings from 1 to 5 into distinct interaction categories: negative, below
average, neutral, above average, and positive.

We conducted an analysis to reveal the inconsistency between users’ social
relationships and their interaction patterns, indicating the presence of
noise. By computing cosine similarity of social relation pairs’ embeddings in
the three datasets, we observed that a certain percentage of user pairs
exhibit low-level similarity (cosine similarity < 0.2), suggesting the
existence of noise in social relationships. Detailed results can be found in
Table 3.

Figure 3. The distribution of social relation pairs across different datasets
based on embedding similarity levels.

####  4.1.2. Evaluation Protocols

In our experiments, we used a 7:1:2 ratio to create training, validation, and
test sets for each dataset, following standard data partitioning criteria in
graph-based recommender systems (wang2019neural, ; he2020lightgcn, ). To
mitigate sampling bias, we employed an all-ranking protocol (lin2022improving,
) to evaluate prediction accuracy for all items. The evaluation metrics used
were Recall@N and NDCG@N, widely adopted in Top-N recommendations.

Table 2. Recommendation performance of all methods in terms of Recall@20 and NDCG@20. Dataset | Metrics | TrustMF | SAMN | DiffNet | GraphRec | DGRec | NGCF | MHCN | KCGN | SMIN | GDMSR | DSL | RecDiff | p-val
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
Ciao | Recall | 0.0539 | 0.0604 | 0.0528 | 0.0540 | 0.0517 | 0.0559 | 0.0621 | 0.0602 | 0.0588 | 0.0560 | 0.0606 | 0.0712 | 4.047-12
Imprv | 32.10% | 17.88% | 34.85% | 31.85% | 37.72% | 27.37% | 14.65% | 18.27% | 21.09% | 27.14% | 17.49% | - | -
NDCG | 0.0343 | 0.0384 | 0.0328 | 0.0335 | 0.0319 | 0.0363 | 0.0378 | 0.0350 | 0.0354 | 0.0355 | 0.0389 | 0.0419 | 4.675-4
Imprv | 22.16% | 9.11% | 27.74% | 25.07% | 31.35% | 15.43% | 10.85% | 19.71% | 18.36% | 18.03% | 7.71% | - | -
Yelp | Recall | 0.0371 | 0.0403 | 0.0557 | 0.0419 | 0.0410 | 0.0450 | 0.0567 | 0.0460 | 0.0485 | 0.0513 | 0.0504 | 0.0597 | 4.288-10
Imprv | 60.92% | 48.14% | 7.18% | 42.48% | 45.61% | 32.67% | 5.29% | 29.78% | 23.09% | 16.37% | 18.45% | - | -
NDCG | 0.0193 | 0.0208 | 0.0292 | 0.0201 | 0.0209 | 0.0230 | 0.0292 | 0.0234 | 0.0251 | 0.0246 | 0.0259 | 0.0308 | 5.064-08
Imprv | 59.59% | 48.08% | 5.48% | 53.23% | 47.37% | 33.91% | 5.48% | 31.62% | 22.71% | 25.20% | 18.92% | - | -
Epinions | Recall | 0.0265 | 0.0329 | 0.0384 | 0.0334 | 0.0326 | 0.0353 | 0.0438 | 0.0370 | 0.0333 | 0.0368 | 0.0365 | 0.0460 | 1.117-08
Imprv | 73.58% | 39.82% | 19.79% | 37.72% | 41.10% | 30.31% | 5.02% | 24.32% | 38.14% | 25.00% | 26.03% | - | -
NDCG | 0.0195 | 0.0226 | 0.0273 | 0.0246 | 0.0236 | 0.0243 | 0.0321 | 0.0264 | 0.0228 | 0.0241 | 0.0267 | 0.0336 | 4.200-08
Imprv | 72.31% | 48.67% | 23.08% | 36.59% | 42.37% | 38.27% | 4.67% | 27.27% | 47.37% | 39.42% | 25.84% | - | -

####  4.1.3. Compared Baselines

We compared our proposed model with 11 baseline methods representing diverse
research approaches. The baseline methods used for comparison include:

(i) Conventional and Attention-based Social Recommenders:

$\bullet$ TrustMF (yang2016social, ): Joint matrix factorization for user-item
interaction and user-user trust matrices to enhance collaborative
recommendations. $\bullet$ SAMN (chen2019social, ): Two-stage attention
mechanism modeling social-aware relations between users and their social
neighbors.

(ii) Graph Collaborative Filtering Models:

$\bullet$ NGCF (wang2019neural, ): A representative graph-enhanced
collaborative filtering model that captures collaborative signals by
propagating embeddings on GCN-layers using a user-item bipartite graph.

(iii) GNN-based Social Recommender Systems:

$\bullet$ GraphRec (fan2019graph, ): Introduces a graph attention network for
attentive information propagation on the social network, merging social
connection and user-item interaction information to enhance user
representations. $\bullet$ DiffNet (wu2019neural, ): Utilizes a layer-wise
diffusion architecture to represent social relations through graph information
propagation, capturing recursive social influences. $\bullet$
GDMSR(quan2023robust, ): Presents a robust graph-based denoising framework
that effectively filters out noise, improving recommendation quality through
preference guidance and relational modeling.

(iv) Temporal-aware Social Recommendation Frameworks:

$\bullet$ DGRec (song2019session, ): Combines RNNs with graph attention layers
to capture dynamic user interests and social connections.

(v) Knowledge-enhanced Social Recommender Systems:

$\bullet$ KCGN (huang2021knowledge, ): Integrates interdependent knowledge
among items and social influences among users within a multi-task learning
framework for social recommendation.

(vi) Self-Supervised Learning Social Recommenders:

$\bullet$ MHCN (yu2021self, ): Self-supervised learning with multi-channel
hypergraph neural networks to enhance model performance. $\bullet$ SMIN
(long2021social, ): Proposes a meta-path-guided heterogeneous graph learning
approach with self-supervised signals based on mutual information maximization
to enhance training in social recommendation. $\bullet$ DSL(wang2023denoised,
): Introduces an adaptive self-supervision task for personalized social
information denoising, preserving valuable social relationships for user
preference modeling.

####  4.1.4. _Hyperparameter Settings_

We implement RecDiff using PyTorch and optimize it with the Adam algorithm.
The embeddings’ dimensionality is tuned from ${8,16,32,64}$. The learning rate
ranges from ${0.001,0.005,0.01}$, and the batch size varies between 512 and
4096. The number of diffusion steps ranges from 10 to 200. Timestep embedding
size is selected from ${4,8,16,32}$. Other hyperparameter details can be found
in our release code. For baselines, we use released code or implement them
based on the original paper. Hyperparameters are optimized through grid
search, with a standardized embedding dimension of 64. The batch size for Ciao
is 2048, while for Yelp and Epinions, it is 4096. GNN models use 1 to 3
propagation layers for optimal performance across baselines.

###  4.2. Overall Performance Comparison (RQ1)

Table 3. Recommendation performance with varying top-N settings, in terms of Recall@N and NDCG@N. Model | Ciao@ 10 | Ciao@ 40 | Yelp@ 10 | Yelp@ 40 | Epinions @ 10 | Epinions @ 40
---|---|---|---|---|---|---
Recall | NDCG | Recall | NDCG | Recall | NDCG | Recall | NDCG | Recall | NDCG | Recall | NDCG
TrustMF | 0.0341 | 0.0289 | 0.0796 | 0.0416 | 0.0224 | 0.0149 | 0.0606 | 0.0254 | 0.0165 | 0.0163 | 0.0394 | 0.0236
SAMN | 0.0345 | 0.0289 | 0.0801 | 0.0429 | 0.0289 | 0.0195 | 0.0700 | 0.0308 | 0.0193 | 0.0181 | 0.0496 | 0.0280
DiffNet | 0.0328 | 0.0271 | 0.0780 | 0.0397 | 0.0381 | 0.0247 | 0.0739 | 0.0312 | 0.0238 | 0.0227 | 0.0587 | 0.0335
GraphRec | 0.0322 | 0.0266 | 0.0838 | 0.0420 | 0.0233 | 0.0144 | 0.0711 | 0.0277 | 0.0207 | 0.0206 | 0.0521 | 0.0304
DGRec | 0.0296 | 0.0254 | 0.0733 | 0.0381 | 0.0245 | 0.0158 | 0.0656 | 0.0272 | 0.0197 | 0.0194 | 0.0517 | 0.0293
NGCF | 0.0366 | 0.0301 | 0.0804 | 0.0343 | 0.0276 | 0.0177 | 0.0711 | 0.0297 | 0.0217 | 0.0206 | 0.0550 | 0.0304
MHCN | 0.0343 | 0.0286 | 0.0929 | 0.0473 | 0.0342 | 0.0225 | 0.0890 | 0.0377 | 0.0272 | 0.0272 | 0.0674 | 0.0321
KCGN | 0.0360 | 0.0263 | 0.0926 | 0.0448 | 0.0284 | 0.0182 | 0.0702 | 0.0295 | 0.0221 | 0.0219 | 0.056 | 0.0325
SMIN | 0.0326 | 0.0275 | 0.0813 | 0.0453 | 0.0316 | 0.0198 | 0.0768 | 0.0312 | 0.0203 | 0.0186 | 0.0531 | 0.0289
GDMSR | 0.0340 | 0.276 | 0.0804 | 0.0409 | 0.0369 | 0.0196 | 0.0744 | 0.0293 | 0.0226 | 0.0206 | 0.0536 | 0.0291
DSL | 0.0412 | 0.0329 | 0.0873 | 0.0473 | 0.0315 | 0.0203 | 0.0786 | 0.0332 | 0.0229 | 0.0226 | 0.0594 | 0.0338
RecDiff | 0.0457 | 0.0361 | 0.1023 | 0.0535 | 0.0391 | 0.0249 | 0.0941 | 0.0394 | 0.0282 | 0.0275 | 0.0696 | 0.0343

We compare the overall recommendation performance of our RecDiff with
baselines. The comparison results are presented in Table 2 for top-20
evaluation and Table 3 for varying top-N evaluation. Based on these results,
we draw the following conclusions.

$\bullet$ Superiority of RecDiff. Our RecDiff consistently outperforms state-
of-the-art baselines, demonstrating superior recommendation accuracy. T-tests
confirm the statistical significance of our results across all datasets and
evaluation metrics. The performance advantage of RecDiff remains consistent
across different top-N settings (Table 3). Our diffusion-based social relation
denoising module removes irrelevant and false information, allowing RecDiff to
effectively mine valuable social ties for enhanced recommendations.

$\bullet$ Negative Impact of Noisy Social Information. Some social
recommendation methods, such as DGRec, DiffNet, and GraphRec, perform worse
than the social information-agnostic method NGCF. This suggests that social
connections can have a negative influence on user-item relation modeling due
to false or irrelevant components. Our RecDiff framework addresses this issue
by denoising social information and consistently outperforms the baseline
model GDMSR. It effectively filters out noise from social connections and
identifies meaningful and influential social ties, accurately encoding user
preferences for precise recommendations.

$\bullet$ Advantages of diffusion-based supervision augmentation. Baseline
methods incorporating self-supervised learning (SSL) consistently outperform
other approaches in recommendation performance. Methods like MHCN, KCGN, and
SMIN utilize variations of the local-global infomax technique, while DSL
employs a prediction alignment SSL task. This highlights the positive impact
of auxiliary supervision signals in addressing data deficiency challenges in
social recommendation, such as noise and sparsity. In contrast, our RecDiff
introduces a multi-step denoising method based on the diffusion model,
generating a larger number of supervision signals at different noise levels.
This robust denoising capability leads to superior recommendation performance,
surpassing the baselines.

###  4.3. Model Ablation Study (RQ2)

In this section, we investigate the influence of different sub-modules in our
RecDiff framework through an ablation study. We evaluate the performance of
several variants obtained by removing or replacing essential modules. The
following ablated models are compared:

$\bullet$ -D: Removes the holistic diffusion module, retaining only the social
and user-item relation learning GNN.

$\bullet$ -S: Does not utilize social information. Instead, it solely relies
on the user-item interaction graph to make recommendations.

$\bullet$ DAE: Replaces the diffusion-based denoising module of RecDiff with a
denoising autoencoder. This DAE-based denoising module is trained to
reconstruct randomly masked user representations.

Figure 4. Ablation studies on Yelp, Ciao, and Epinions datasets for different
sub-modules in our proposed RecDiff framework, measuring Recall@20 and
NDCG@20.

We evaluate these variants on the Ciao and Yelp datasets using the top-20
recommendation setting. The results, depicted in Figure 4, consistently
demonstrate that RecDiff outperforms all four variants. These findings
strongly support the effectiveness of the social relation learning and
diffusion-based denoising components in our model. Notable observations from
our analysis include:

$\bullet$ (1) Removing the diffusion module (-D) leads to significant
performance degradation, highlighting the denoising function’s effectiveness
provided by our latent feature-level diffusion model.

$\bullet$ (2) Comparing the -S variant to RecDiff highlights the significant
improvement obtained by incorporating users’ social context information in
user preference learning. However, subgraphs (b) and (e) suggest that in the
presence of noisy social information in the epinions dataset, the -S variant
may outperform the -D variant.

$\bullet$ (3) The suboptimal performance of the DAE variant showcases the
superior denoising ability of our designed diffusion module compared to
vanilla denoising techniques. RecDiff effectively models complex
representation distributions by gradually learning each denoising transition
step from $t$ to $t-1$ through shared neural networks, enhancing noise
reduction in latent features.

###  4.4. Impact of Hyperparameters (RQ3)

This section investigates the impact of crucial hyperparameters on model
performance: the dimensionality of hidden representations ($d$), the
dimensionality of time step embeddings ($d^{\prime}$), and the maximum number
of diffusion steps ($T$). Evaluation is conducted on all three experimental
datasets, measuring Recall@20 and NDCG@20 metrics. The results, shown in
Figure 6, are analyzed as follows:

$\bullet$ Embedding dimensionality $d$: Increasing $d$ improves performance,
except for the Ciao and Epinions datasets where larger values lead to slight
degradation due to overfitting.

$\bullet$ Time step embedding size $d^{\prime}$: Larger dimensions enhance the
positive impact of diffusion steps on denoising, improving performance.
However, excessively high dimensions hinder the model’s diffusion ability,
resulting in decreased performance.

$\bullet$ Maximum diffusion steps $T$: Increasing $T$ enhances performance
with more diffusion steps. However, extremely large values damage social
information and reduce denoising effectiveness.

###  4.5. Impact of Noise Scale (RQ4)

This section investigates the impact of the noise scale factor ($\tau$) on our
noising process. By adjusting the minimum noise ($\bar{s}{min}$) and maximum
noise ($\bar{s}{max}$) in the noise scheduler to $\tau\cdot\bar{s}{min}$ and
$\tau\cdot\bar{s}{max}$, respectively, we examine the model’s performance with
different noise scale values of ${1,0.1,0.01,0.001}$. The results, depicted in
Figure 5, reveal the following insights:

$\bullet$ Increasing the noise scale effectively improves model performance,
showcasing the effectiveness of our denoising mechanism within our proposed
RecDiff framework.

$\bullet$ Further increasing the noise scale beyond a certain threshold leads
to a decline in performance. This effect is particularly pronounced in
sparsely populated datasets like Yelp and Epinion.

We attribute this decline to excessive noise obscuring the intrinsic
personalized data, thereby hindering the model’s ability to retain and process
essential individualized information.

Figure 5. Impact of noise scale over model performance. Figure 6.
Hyperparameter study on important parametric configurations of RecDiff, in
terms of Recall@20 and NDCG@20.

###  4.6. Training Efficiency Study (RQ5)

This section optimizes the efficiency of our RecDiff compared to baseline
models (MHCN, SMIN, and KCGN) on the Ciao and Yelp datasets. Using an A40
graphics card with 48GB of GPU memory, we compared the time costs of these
baselines (Table 4). Our RecDiff demonstrates significant efficiency
advantages in both training and testing. For each training epoch, we evaluated
and recorded the test set performance to analyze improvements (Figure 8).

$\bullet$ Training efficiency of RecDiff: Our RecDiff consistently outperforms
the baselines in training efficiency, benefiting from effective denoising
diffusion for accelerated optimization.

$\bullet$ Limitations of baselines: SMIN shows overfitting effects,
potentially due to reliance on metagraphs, limiting generalization. MHCN
achieves high final performance but converges slower due to its complex
hypergraph structure. In contrast, our RecDiff benefits from a compact neural
architecture without handcrafted priors, enabling faster optimization with
auxiliary signals.

$\bullet$ Fluctuations on Ciao data: In comparing convergence curves,
significant recommendation performance fluctuations are observed on the
smaller Ciao dataset, indicating training instability.

###  4.7. Further Exploration of Anti-Noise Capacity with our RecDiff
Framework (RQ6)

We evaluate the robustness of RecDiff in the presence of data noise by
introducing random fake edges to replace varying percentages of genuine social
connections in the user-user graph. The model is then retrained using the
corrupted graph and evaluated on the true test set. Specifically, we analyze
the effects of replacing 0%, 20%, and 50% of the social relations with noise
signals. Comparing the performance of RecDiff with MHCN and DiffNet, the
results in Figure 9 (a) and (b) show the original evaluation outcomes, while
(c) illustrates the relative performance change in NDCG. Based on these
results, the following observations are made:

$\bullet$ Advantageous robustness of RecDiff: Our RecDiff model outperforms
the baselines with a smaller performance drop, showcasing its superior
denoising capabilities in social recommendation.

$\bullet$ Denoising effect of vanilla SSL: The MHCN model shows promise in
denoising, but it falls short compared to our RecDiff model. This highlights
that general-purpose self-supervised learning tasks may not effectively
address the specific denoising requirements of social recommendation.

$\bullet$ Higher noise ratio in Ciao dataset: The Ciao dataset demonstrates a
larger performance drop, suggesting a higher noise ratio in comparison to
other datasets.

Figure 7. Case study for the user relation recalibration effect of our social
denoiser RecDiff.

Figure 8. Model performance by training epochs on the Ciao and Yelp test sets,
measured by Recall@20 and NDCG@20. Table 4. The running time (in seconds) per
epoch for different models is compared on diverse evaluation datasets.

Model | Training | Testing
---|---|---
ciao | yelp | epinions | ciao | yelp | epinions
MHCN | 0.46 | 28.51 | 9.98 | 0.33 | 44.39 | 22.74
KCGN | 0.33 | 75.84 | 63.11 | 0.25 | 31.23 | 13.61
SMIN | 0.95 | 60.86 | 66.15 | 1.25 | 35.54 | 27.42
Ours | 0.19 | 4.23 | 2.78 | 0.31 | 27.91 | 13.54

Figure 9. Investigating the Influence of Different Noise Ratios on Performance
Degradation.

###  4.8. Case Study (RQ7)

This section explores the denoising effect of RecDiff on specific user/item
cases. Four subgraph cases are illustrated in Figure 7, highlighting the need
for denoising. The baseline methods, KCGN and MHCN, fail to identify false
social connections, resulting in high cosine scores for the incorrect social
neighbors. In contrast, our proposed RecDiff effectively recognizes these
noise instances, yielding significantly lower similarity scores and producing
distinct embeddings for falsely-connected users. These findings demonstrate
the superior noise elimination capability of RecDiff across different noise
situations.

Two additional cases are presented, involving user pairs sharing interactions
with items that significantly differ in category from other items the users
interact with. These isolated interactions are likely to be noisy items,
rendering the associated social links noisy as well. Once again, RecDiff
successfully identifies and eliminates the noise, assigning lower similarity
scores and generating more distinct embeddings for false social neighbors.
These cases further exemplify the denoising effectiveness of our RecDiff
approach.

##  5\. Related Work

$\bullet$ Social-aware Recommender Systems. Deep learning-based social
recommender systems, such as DiffNet (wu2019neural, ), RecoGCN
(xu2019relation, ), and KCGN (huang2021knowledge, ), leverage Graph Neural
Networks to effectively model the connections between users and items.
Approaches like SAMN (chen2019social, ) and GraphRec (fan2019graph, ) further
enhance social recommendation by incorporating attention mechanisms to
differentially differentiate the influence levels among users. More recent
self-supervised learning (SSL) based methods, including MHCN (yu2021self, ),
SMIN (long2021social, ), SDCRec (du2022socially, ), and DcRec
(wu2022disentangled, ), have shown promising and encouraging results in
bolstering social recommenders through innovative SSL-based data augmentation
techniques. In contrast to these existing established approaches, our proposed
method, RecDiff, takes a unique and distinctive stance by concentrating on
denoising relation learning in social recommender systems with the power of
diffusion models.

$\bullet$ Recommendation with Graph Neural Networks. Graph neural networks
have achieved state-of-the-art performance in recommendation scenarios
(yan20222, ; higpt2024, ; zhou2023layer, ). Ealier works like NGCF
(wang2019neural, ) and Pinsage (ying2018graph, ) introduced higher-order
connectivity extraction using graph convolutional networks (GCNs). LightGCN
(he2020lightgcn, ) simplified training by removing non-linear activations,
while DGCF (wang2020disentangled, ) focused on intent-aware modeling through
graph disentangling. Studies have also incorporated auxiliary information,
such as multi-modal (wei2019mmgcn, ) and knowledge (wang2019kgat, ) data, to
further enhance recommendation performance. Recent advancements in graph self-
supervised learning include SGL (wu2021self, ), AutoCF (autocfwww2023, ), and
NCL (lin2022improving, ), which have demonstrated promising results. In
contrast, our work takes a unique approach by enhancing the denoising
capabilities of recommenders through the development of an auxiliary task for
social recommendation, leveraging a diffusion-based paradigm.

$\bullet$ Generative Models for Recommendation. Generative models, such as
GANs (wang2017irgan, ) and VAEs (Yu_Zhang_Cao_Xia, ), have gained prominence
in recommender systems for data generation to enhance preference modeling
(liu2021interest, ; Wei_Wang_Nie_Li_Wang_Chua_2022, ). Some approaches focus
on generating synthetic user-item interaction data to address data sparsity
and cold start issues. GAN-based methods (Chen_Wang_Huang_Huang_Xu_Lin_Inc_Li,
; jin2020sampling, ; Wang_Ye_Chen_Zhang_Wang_Zou_Liu_Wang_Wang_Generative, )
use adversarial training to mimic real user behaviors. VAE-based generative
recommendation models (liang2018variational, ; Ma_Zhou_Cui_Yang_Zhu_2019, )
employ variational autoencoders to make accurate predictions. More recently,
studies have explored the use of diffusion models (austin2021structured, ;
Croitoru_Hondru_Ionescu_Shah_2022, ; popov2021grad, ) for improved data
generation. For example, DiffRec (wang2023diffusion, ) and DiffKG (diffkgwsdm,
) use diffusion models to denoise the interaction data and knowledge graph,
respectively, leading to enhanced recommendation performance.

In contrast, our work takes a distinct approach. RecDiff leverages diffusion
models’ denoising paradigm to refine social representations for
recommendation. It encodes structural features of the social graph into low-
dimensional embeddings and performs denoising with a hidden-space diffusion
paradigm.

##  6\. Conclusion

This paper aims to enhance social-aware recommender systems by eliminating
false or irrelevant user-wise social links. To achieve this goal, we propose
RecDiff, a novel diffusion model that trains a social denoiser through a
multi-step noise propagation and elimination task. This diffusion process
operates in the hidden space, utilizing encoded user representations for both
effectiveness and simplicity. By training the model with varying diffusion
steps, RecDiff demonstrates exceptional capabilities in handling diverse noisy
effects. We evaluate the effectiveness of our model through experiments on
real-world datasets, showing significant improvements in recommendation
accuracy compared to existing methods. In the future, we plan to explore the
potential of our model in diverse recommendation scenarios, incorporating
multi-modal information.

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