#
DEIS

Fast Sampling of Diffusion Models with Exponential Integrator.

##
Overview

Original paper can be found here. The original implementation can be found here.

##
DEISMultistepScheduler

###
class diffusers.DEISMultistepScheduler

< source >

( num_train_timesteps: int = 1000 beta_start: float = 0.0001 beta_end: float = 0.02 beta_schedule: str = 'linear' trained_betas: typing.Optional[numpy.ndarray] = None solver_order: int = 2 prediction_type: str = 'epsilon' thresholding: bool = False dynamic_thresholding_ratio: float = 0.995 sample_max_value: float = 1.0 algorithm_type: str = 'deis' solver_type: str = 'logrho' lower_order_final: bool = True use_karras_sigmas: typing.Optional[bool] = False timestep_spacing: str = 'linspace' steps_offset: int = 0 )

Parameters

- num_train_timesteps (`int`) — number of diffusion steps used to train the model.
- beta_start (`float`) — the starting `beta` value of inference.
- beta_end (`float`) — the final `beta` value.
- beta_schedule (`str`) — the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
- trained_betas (`np.ndarray`, optional) — option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
- solver_order (`int`, default `2`) — the order of DEIS; can be `1` or `2` or `3`. We recommend to use `solver_order=2` for guided sampling, and `solver_order=3` for unconditional sampling.
- prediction_type (`str`, default `epsilon`) — indicates whether the model predicts the noise (epsilon), or the data / `x0`. One of `epsilon`, `sample`, or `v-prediction`.
- thresholding (`bool`, default `False`) — whether to use the “dynamic thresholding” method (introduced by Imagen, https://arxiv.org/abs/2205.11487). Note that the thresholding method is unsuitable for latent-space diffusion models (such as stable-diffusion).
- dynamic_thresholding_ratio (`float`, default `0.995`) — the ratio for the dynamic thresholding method. Default is `0.995`, the same as Imagen (https://arxiv.org/abs/2205.11487).
- sample_max_value (`float`, default `1.0`) — the threshold value for dynamic thresholding. Valid only when `thresholding=True`
- algorithm_type (`str`, default `deis`) — the algorithm type for the solver. current we support multistep deis, we will add other variants of DEIS in the future
- lower_order_final (`bool`, default `True`) — whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. We empirically find this trick can stabilize the sampling of DEIS for steps < 15, especially for steps <= 10.
- use_karras_sigmas (`bool`, optional, defaults to `False`) — This parameter controls whether to use Karras sigmas (Karras et al. (2022) scheme) for step sizes in the noise schedule during the sampling process. If True, the sigmas will be determined according to a sequence of noise levels {σi} as defined in Equation (5) of the paper https://arxiv.org/pdf/2206.00364.pdf.
- timestep_spacing (`str`, default `"linspace"`) — The way the timesteps should be scaled. Refer to Table 2. of Common Diffusion Noise Schedules and Sample Steps are Flawed for more information.
- steps_offset (`int`, default `0`) — an offset added to the inference steps. You can use a combination of `offset=1` and `set_alpha_to_one=False`, to make the last step use step 0 for the previous alpha product, as done in stable diffusion.

DEIS (https://arxiv.org/abs/2204.13902) is a fast high order solver for diffusion ODEs. We slightly modify the polynomial fitting formula in log-rho space instead of the original linear t space in DEIS paper. The modification enjoys closed-form coefficients for exponential multistep update instead of replying on the numerical solver. More variants of DEIS can be found in https://github.com/qsh-zh/deis.

Currently, we support the log-rho multistep DEIS. We recommend to use `solver_order=2 / 3` while `solver_order=1` reduces to DDIM.

We also support the “dynamic thresholding” method in Imagen (https://arxiv.org/abs/2205.11487). For pixel-space diffusion models, you can set `thresholding=True` to use the dynamic thresholding.

~ConfigMixin takes care of storing all config attributes that are passed in the scheduler’s `__init__` function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`. SchedulerMixin provides general loading and saving functionality via the SchedulerMixin.save_pretrained() and from_pretrained() functions.

####
convert_model_output

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( model_output: FloatTensor timestep: int sample: FloatTensor ) → `torch.FloatTensor`

Parameters

- model_output (`torch.FloatTensor`) — direct output from learned diffusion model.
- timestep (`int`) — current discrete timestep in the diffusion chain.
- sample (`torch.FloatTensor`) — current instance of sample being created by diffusion process.

Returns

`torch.FloatTensor`

the converted model output.

Convert the model output to the corresponding type that the algorithm DEIS needs.

####
deis_first_order_update

< source >

( model_output: FloatTensor timestep: int prev_timestep: int sample: FloatTensor ) → `torch.FloatTensor`

Parameters

- model_output (`torch.FloatTensor`) — direct output from learned diffusion model.
- timestep (`int`) — current discrete timestep in the diffusion chain.
- prev_timestep (`int`) — previous discrete timestep in the diffusion chain.
- sample (`torch.FloatTensor`) — current instance of sample being created by diffusion process.

Returns

`torch.FloatTensor`

the sample tensor at the previous timestep.

One step for the first-order DEIS (equivalent to DDIM).

####
multistep_deis_second_order_update

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( model_output_list: typing.List[torch.FloatTensor] timestep_list: typing.List[int] prev_timestep: int sample: FloatTensor ) → `torch.FloatTensor`

Parameters

- model_output_list (`List[torch.FloatTensor]`) — direct outputs from learned diffusion model at current and latter timesteps.
- timestep (`int`) — current and latter discrete timestep in the diffusion chain.
- prev_timestep (`int`) — previous discrete timestep in the diffusion chain.
- sample (`torch.FloatTensor`) — current instance of sample being created by diffusion process.

Returns

`torch.FloatTensor`

the sample tensor at the previous timestep.

One step for the second-order multistep DEIS.

####
multistep_deis_third_order_update

< source >

( model_output_list: typing.List[torch.FloatTensor] timestep_list: typing.List[int] prev_timestep: int sample: FloatTensor ) → `torch.FloatTensor`

Parameters

- model_output_list (`List[torch.FloatTensor]`) — direct outputs from learned diffusion model at current and latter timesteps.
- timestep (`int`) — current and latter discrete timestep in the diffusion chain.
- prev_timestep (`int`) — previous discrete timestep in the diffusion chain.
- sample (`torch.FloatTensor`) — current instance of sample being created by diffusion process.

Returns

`torch.FloatTensor`

the sample tensor at the previous timestep.

One step for the third-order multistep DEIS.

####
scale_model_input

< source >

( sample: FloatTensor *args **kwargs ) → `torch.FloatTensor`

Parameters

- sample (`torch.FloatTensor`) — input sample

Returns

`torch.FloatTensor`

scaled input sample

Ensures interchangeability with schedulers that need to scale the denoising model input depending on the current timestep.

####
set_timesteps

< source >

( num_inference_steps: int device: typing.Union[str, torch.device] = None )

Parameters

- num_inference_steps (`int`) — the number of diffusion steps used when generating samples with a pre-trained model.
- device (`str` or `torch.device`, optional) — the device to which the timesteps should be moved to. If `None`, the timesteps are not moved.

Sets the timesteps used for the diffusion chain. Supporting function to be run before inference.

####
step

< source >

( model_output: FloatTensor timestep: int sample: FloatTensor return_dict: bool = True ) → `~scheduling_utils.SchedulerOutput` or `tuple`

Parameters

- model_output (`torch.FloatTensor`) — direct output from learned diffusion model.
- timestep (`int`) — current discrete timestep in the diffusion chain.
- sample (`torch.FloatTensor`) — current instance of sample being created by diffusion process.
- return_dict (`bool`) — option for returning tuple rather than SchedulerOutput class

Returns

`~scheduling_utils.SchedulerOutput` or `tuple`

`~scheduling_utils.SchedulerOutput` if `return_dict` is True, otherwise a `tuple`. When returning a tuple, the first element is the sample tensor.

Step function propagating the sample with the multistep DEIS.