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 logrho space instead of the original linear t
space in the DEIS paper. The modification enjoys closedform 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 highfidelity 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 highfidelity 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 pretrained DMs, we achieve the stateofart 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 qshzh/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 pixelspace
diffusion models, you can set thresholding=True
to use the dynamic thresholding.
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
, defaults to 1000) — The number of diffusion steps to train the model. 
beta_start (
float
, defaults to 0.0001) — The startingbeta
value of inference. 
beta_end (
float
, defaults to 0.02) — The finalbeta
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 fromlinear
,scaled_linear
, orsquaredcos_cap_v2
. 
trained_betas (
np.ndarray
, optional) — Pass an array of betas directly to the constructor to bypassbeta_start
andbeta_end
. 
solver_order (
int
, defaults to 2) — The DEIS order which can be1
or2
or3
. It is recommended to usesolver_order=2
for guided sampling, andsolver_order=3
for unconditional sampling. 
prediction_type (
str
, defaults toepsilon
) — Prediction type of the scheduler function; can beepsilon
(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 toFalse
) — Whether to use the “dynamic thresholding” method. This is unsuitable for latentspace diffusion models such as Stable Diffusion. 
dynamic_thresholding_ratio (
float
, defaults to 0.995) — The ratio for the dynamic thresholding method. Valid only whenthresholding=True
. 
sample_max_value (
float
, defaults to 1.0) — The threshold value for dynamic thresholding. Valid only whenthresholding=True
. 
algorithm_type (
str
, defaults todeis
) — The algorithm type for the solver. 
lower_order_final (
bool
, defaults toTrue
) — Whether to use lowerorder solvers in the final steps. Only valid for < 15 inference steps. 
use_karras_sigmas (
bool
, optional, defaults toFalse
) — Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. IfTrue
, 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 ofoffset=1
andset_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
< source >(
model_output: FloatTensor
timestep: int
sample: 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
< source >(
model_output: FloatTensor
timestep: int
prev_timestep: int
sample: 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 firstorder DEIS (equivalent to DDIM).
multistep_deis_second_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]
) — 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 secondorder 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]
) — 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 thirdorder multistep DEIS.
scale_model_input
< source >(
sample: FloatTensor
*args
**kwargs
)
→
torch.FloatTensor
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 )
Sets the discrete timesteps used for the diffusion chain (to be run before inference).
step
< source >(
model_output: FloatTensor
timestep: int
sample: FloatTensor
return_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 ortuple
.
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
< source >( prev_sample: FloatTensor )
Base class for the output of a scheduler’s step
function.