DEISMultistepScheduler

Diffusion Exponential Integrator Sampler (DEIS) is proposed in Fast Sampling of Diffusion Models with Exponential Integrator by Qinsheng Zhang and Yongxin Chen. DEISMultistepScheduler is a fast high order solver for diffusion ordinary differential equations (ODEs).

This implementation modifies the polynomial fitting formula in log-rho space instead of the original linear t space in the DEIS paper. The modification enjoys closed-form coefficients for exponential multistep update instead of replying on the numerical solver.

The abstract from the paper is:

The past few years have witnessed the great success of Diffusion models~(DMs) in generating high-fidelity samples in generative modeling tasks. A major limitation of the DM is its notoriously slow sampling procedure which normally requires hundreds to thousands of time discretization steps of the learned diffusion process to reach the desired accuracy. Our goal is to develop a fast sampling method for DMs with a much less number of steps while retaining high sample quality. To this end, we systematically analyze the sampling procedure in DMs and identify key factors that affect the sample quality, among which the method of discretization is most crucial. By carefully examining the learned diffusion process, we propose Diffusion Exponential Integrator Sampler~(DEIS). It is based on the Exponential Integrator designed for discretizing ordinary differential equations (ODEs) and leverages a semilinear structure of the learned diffusion process to reduce the discretization error. The proposed method can be applied to any DMs and can generate high-fidelity samples in as few as 10 steps. In our experiments, it takes about 3 minutes on one A6000 GPU to generate 50k images from CIFAR10. Moreover, by directly using pre-trained DMs, we achieve the state-of-art sampling performance when the number of score function evaluation~(NFE) is limited, e.g., 4.17 FID with 10 NFEs, 3.37 FID, and 9.74 IS with only 15 NFEs on CIFAR10. Code is available at this https URL.

The original codebase can be found at qsh-zh/deis.

Tips

It is recommended to set solver_order to 2 or 3, while solver_order=1 is equivalent to DDIMScheduler.

Dynamic thresholding from Imagen is supported, and for pixel-space diffusion models, you can set thresholding=True to use the dynamic thresholding.

DEISMultistepScheduler

class diffusers.DEISMultistepScheduler

( num_train_timesteps: int = 1000beta_start: float = 0.0001beta_end: float = 0.02beta_schedule: str = 'linear'trained_betas: typing.Optional[numpy.ndarray] = Nonesolver_order: int = 2prediction_type: str = 'epsilon'thresholding: bool = Falsedynamic_thresholding_ratio: float = 0.995sample_max_value: float = 1.0algorithm_type: str = 'deis'solver_type: str = 'logrho'lower_order_final: bool = Trueuse_karras_sigmas: typing.Optional[bool] = Falsetimestep_spacing: str = 'linspace'steps_offset: int = 0 )

Parameters

num_train_timesteps (int, defaults to 1000) — The number of diffusion steps to train the model.
beta_start (float, defaults to 0.0001) — The starting beta value of inference.
beta_end (float, defaults to 0.02) — The final beta value.
beta_schedule (str, defaults to "linear") — 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) — Pass an array of betas directly to the constructor to bypass beta_start and beta_end.
solver_order (int, defaults to 2) — The DEIS order which can be 1 or 2 or 3. It is recommended to use solver_order=2 for guided sampling, and solver_order=3 for unconditional sampling.
prediction_type (str, defaults to epsilon) — Prediction type of the scheduler function; can be epsilon (predicts the noise of the diffusion process), sample (directly predicts the noisy sample) or v_prediction` (see section 2.4 of Imagen Video paper).
thresholding (bool, defaults to False) — Whether to use the “dynamic thresholding” method. This is unsuitable for latent-space diffusion models such as Stable Diffusion.
dynamic_thresholding_ratio (float, defaults to 0.995) — The ratio for the dynamic thresholding method. Valid only when thresholding=True.
sample_max_value (float, defaults to 1.0) — The threshold value for dynamic thresholding. Valid only when thresholding=True.
algorithm_type (str, defaults to deis) — The algorithm type for the solver.
lower_order_final (bool, defaults to True) — Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps.
use_karras_sigmas (bool, optional, defaults to False) — Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If True, the sigmas are determined according to a sequence of noise levels {σi}.
timestep_spacing (str, defaults to "linspace") — The way the timesteps should be scaled. Refer to Table 2 of the Common Diffusion Noise Schedules and Sample Steps are Flawed for more information.
steps_offset (int, defaults to 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 like in Stable Diffusion.

DEISMultistepScheduler is a fast high order solver for diffusion ordinary differential equations (ODEs).

This model inherits from SchedulerMixin and ConfigMixin. Check the superclass documentation for the generic methods the library implements for all schedulers such as loading and saving.

convert_model_output

( model_output: FloatTensortimestep: intsample: FloatTensor ) → torch.FloatTensor

Parameters

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

Returns

torch.FloatTensor

The converted model output.

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

deis_first_order_update

( model_output: FloatTensortimestep: intprev_timestep: intsample: FloatTensor ) → torch.FloatTensor

Parameters

model_output (torch.FloatTensor) — The direct output from the learned diffusion model.
timestep (int) — The current discrete timestep in the diffusion chain.
prev_timestep (int) — The previous discrete timestep in the diffusion chain.
sample (torch.FloatTensor) — A current instance of a sample created by the 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

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

Parameters

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

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

Parameters

model_output_list (List[torch.FloatTensor]) — The direct outputs from learned diffusion model at current and latter timesteps.
timestep (int) — The current and latter discrete timestep in the diffusion chain.
prev_timestep (int) — The previous discrete timestep in the diffusion chain.
sample (torch.FloatTensor) — A current instance of a sample 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

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

Parameters

sample (torch.FloatTensor) — The input sample.

Returns

torch.FloatTensor

A scaled input sample.

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

set_timesteps

( num_inference_steps: intdevice: 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 discrete timesteps used for the diffusion chain (to be run before inference).

step

( model_output: FloatTensortimestep: intsample: FloatTensorreturn_dict: bool = True ) → SchedulerOutput or tuple

Parameters

model_output (torch.FloatTensor) — The direct output from learned diffusion model.
timestep (float) — The current discrete timestep in the diffusion chain.
sample (torch.FloatTensor) — A current instance of a sample created by the diffusion process.
return_dict (bool) — Whether or not to return a SchedulerOutput or tuple.

Returns

SchedulerOutput or tuple

If return_dict is True, SchedulerOutput is returned, otherwise a tuple is returned where the first element is the sample tensor.

Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with the multistep DEIS.

SchedulerOutput

class diffusers.schedulers.scheduling_utils.SchedulerOutput

( prev_sample: FloatTensor )

Parameters

prev_sample (torch.FloatTensor of shape (batch_size, num_channels, height, width) for images) — Computed sample (x_{t-1}) of previous timestep. prev_sample should be used as next model input in the denoising loop.

Base class for the output of a scheduler’s step function.

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