DEISMultistepScheduler
Last updated
Last updated
Diffusion Exponential Integrator Sampler (DEIS) is proposed in 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 .
The original codebase can be found at .
It is recommended to set solver_order to 2 or 3, while solver_order=1 is equivalent to .
Dynamic thresholding from is supported, and for pixel-space diffusion models, you can set thresholding=True to use the dynamic thresholding.
( 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) β The number of diffusion steps to train the model.
beta_start (float, defaults to 0.0001) β The starting beta value of inference.
beta_end (float, defaults to 0.02) β The final beta value.
beta_schedule (str, defaults to "linear") β 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) β Pass an array of betas directly to the constructor to bypass beta_start and beta_end.
solver_order (int, defaults to 2) β 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) β 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 paper).
thresholding (bool, defaults to False) β Whether to use the βdynamic thresholdingβ method. This is unsuitable for latent-space diffusion models such as Stable Diffusion.
dynamic_thresholding_ratio (float, defaults to 0.995) β The ratio for the dynamic thresholding method. Valid only when thresholding=True.
sample_max_value (float, defaults to 1.0) β The threshold value for dynamic thresholding. Valid only when thresholding=True.
algorithm_type (str, defaults to deis) β The algorithm type for the solver.
lower_order_final (bool, defaults to True) β Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps.
use_karras_sigmas (bool, optional, defaults to False) β 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 {Οi}.
timestep_spacing (str, defaults to "linspace") β The way the timesteps should be scaled. Refer to Table 2 of the for more information.
steps_offset (int, defaults to 0) β 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).
convert_model_output
( model_output: FloatTensortimestep: intsample: FloatTensor ) β torch.FloatTensor
Parameters
model_output (torch.FloatTensor) β The direct output from the learned diffusion model.
timestep (int) β The current discrete timestep in the diffusion chain.
sample (torch.FloatTensor) β 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 ) β torch.FloatTensor
Parameters
model_output (torch.FloatTensor) β The direct output from the learned diffusion model.
timestep (int) β The current discrete timestep in the diffusion chain.
prev_timestep (int) β The previous discrete timestep in the diffusion chain.
sample (torch.FloatTensor) β 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 ) β torch.FloatTensor
Parameters
model_output_list (List[torch.FloatTensor]) β The direct outputs from learned diffusion model at current and latter timesteps.
timestep (int) β The current and latter discrete timestep in the diffusion chain.
prev_timestep (int) β The previous discrete timestep in the diffusion chain.
sample (torch.FloatTensor) β 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 ) β torch.FloatTensor
Parameters
model_output_list (List[torch.FloatTensor]) β The direct outputs from learned diffusion model at current and latter timesteps.
timestep (int) β The current and latter discrete timestep in the diffusion chain.
prev_timestep (int) β The previous discrete timestep in the diffusion chain.
sample (torch.FloatTensor) β 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 ) β torch.FloatTensor
Parameters
sample (torch.FloatTensor) β 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) β The number of diffusion steps used when generating samples with a pre-trained model.
device (str or torch.device, optional) β 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
Parameters
model_output (torch.FloatTensor) β The direct output from learned diffusion model.
timestep (float) β The current discrete timestep in the diffusion chain.
sample (torch.FloatTensor) β A current instance of a sample created by the diffusion process.
Returns
Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with the multistep DEIS.
( prev_sample: FloatTensor )
Parameters
prev_sample (torch.FloatTensor of shape (batch_size, num_channels, height, width) for images) β 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 schedulerβs step function.
This model inherits from and . Check the superclass documentation for the generic methods the library implements for all schedulers such as loading and saving.
( model_output: FloatTensortimestep: intsample: FloatTensorreturn_dict: bool = True ) β or tuple
return_dict (bool) β Whether or not to return a or tuple.
or tuple
If return_dict is True, is returned, otherwise a tuple is returned where the first element is the sample tensor.