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-rw-r--r--schedulers/scheduling_deis_multistep.py500
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1# Copyright 2022 FLAIR Lab and The HuggingFace Team. All rights reserved.
2#
3# Licensed under the Apache License, Version 2.0 (the "License");
4# you may not use this file except in compliance with the License.
5# You may obtain a copy of the License at
6#
7# http://www.apache.org/licenses/LICENSE-2.0
8#
9# Unless required by applicable law or agreed to in writing, software
10# distributed under the License is distributed on an "AS IS" BASIS,
11# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12# See the License for the specific language governing permissions and
13# limitations under the License.
14
15# DISCLAIMER: check https://arxiv.org/abs/2204.13902 and https://github.com/qsh-zh/deis for more info
16# The codebase is modified based on https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py
17
18import math
19from typing import List, Optional, Tuple, Union
20
21import numpy as np
22import torch
23
24from diffusers.configuration_utils import ConfigMixin, register_to_config
25from diffusers.schedulers.scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
26
27
28def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999):
29 """
30 Create a beta schedule that discretizes the given alpha_t_bar function, which defines the cumulative product of
31 (1-beta) over time from t = [0,1].
32
33 Contains a function alpha_bar that takes an argument t and transforms it to the cumulative product of (1-beta) up
34 to that part of the diffusion process.
35
36
37 Args:
38 num_diffusion_timesteps (`int`): the number of betas to produce.
39 max_beta (`float`): the maximum beta to use; use values lower than 1 to
40 prevent singularities.
41
42 Returns:
43 betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
44 """
45
46 def alpha_bar(time_step):
47 return math.cos((time_step + 0.008) / 1.008 * math.pi / 2) ** 2
48
49 betas = []
50 for i in range(num_diffusion_timesteps):
51 t1 = i / num_diffusion_timesteps
52 t2 = (i + 1) / num_diffusion_timesteps
53 betas.append(min(1 - alpha_bar(t2) / alpha_bar(t1), max_beta))
54 return torch.tensor(betas, dtype=torch.float32)
55
56
57class DEISMultistepScheduler(SchedulerMixin, ConfigMixin):
58 """
59 DEIS (https://arxiv.org/abs/2204.13902) is a fast high order solver for diffusion ODEs. We slightly modify the
60 polynomial fitting formula in log-rho space instead of the original linear t space in DEIS paper. The modification
61 enjoys closed-form coefficients for exponential multistep update instead of replying on the numerical solver. More
62 variants of DEIS can be found in https://github.com/qsh-zh/deis.
63
64 Currently, we support the log-rho multistep DEIS. We recommend to use `solver_order=2 / 3` while `solver_order=1`
65 reduces to DDIM.
66
67 We also support the "dynamic thresholding" method in Imagen (https://arxiv.org/abs/2205.11487). For pixel-space
68 diffusion models, you can set `thresholding=True` to use the dynamic thresholding.
69
70 [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
71 function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
72 [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and
73 [`~SchedulerMixin.from_pretrained`] functions.
74
75 Args:
76 num_train_timesteps (`int`): number of diffusion steps used to train the model.
77 beta_start (`float`): the starting `beta` value of inference.
78 beta_end (`float`): the final `beta` value.
79 beta_schedule (`str`):
80 the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
81 `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
82 trained_betas (`np.ndarray`, optional):
83 option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
84 solver_order (`int`, default `2`):
85 the order of DEIS; can be `1` or `2` or `3`. We recommend to use `solver_order=2` for guided sampling, and
86 `solver_order=3` for unconditional sampling.
87 prediction_type (`str`, default `epsilon`):
88 indicates whether the model predicts the noise (epsilon), or the data / `x0`. One of `epsilon`, `sample`,
89 or `v-prediction`.
90 thresholding (`bool`, default `False`):
91 whether to use the "dynamic thresholding" method (introduced by Imagen, https://arxiv.org/abs/2205.11487).
92 Note that the thresholding method is unsuitable for latent-space diffusion models (such as
93 stable-diffusion).
94 dynamic_thresholding_ratio (`float`, default `0.995`):
95 the ratio for the dynamic thresholding method. Default is `0.995`, the same as Imagen
96 (https://arxiv.org/abs/2205.11487).
97 sample_max_value (`float`, default `1.0`):
98 the threshold value for dynamic thresholding. Valid woks when `thresholding=True`
99 algorithm_type (`str`, default `deis`):
100 the algorithm type for the solver. current we support multistep deis, we will add other variants of DEIS in
101 the future
102 lower_order_final (`bool`, default `True`):
103 whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. We empirically
104 find this trick can stabilize the sampling of DEIS for steps < 15, especially for steps <= 10.
105
106 """
107
108 _compatibles = [e.name for e in KarrasDiffusionSchedulers]
109 order = 1
110
111 @register_to_config
112 def __init__(
113 self,
114 num_train_timesteps: int = 1000,
115 beta_start: float = 0.0001,
116 beta_end: float = 0.02,
117 beta_schedule: str = "linear",
118 trained_betas: Optional[np.ndarray] = None,
119 solver_order: int = 2,
120 prediction_type: str = "epsilon",
121 thresholding: bool = False,
122 dynamic_thresholding_ratio: float = 0.995,
123 sample_max_value: float = 1.0,
124 algorithm_type: str = "deis",
125 solver_type: str = "logrho",
126 lower_order_final: bool = True,
127 ):
128 if trained_betas is not None:
129 self.betas = torch.tensor(trained_betas, dtype=torch.float32)
130 elif beta_schedule == "linear":
131 self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32)
132 elif beta_schedule == "scaled_linear":
133 # this schedule is very specific to the latent diffusion model.
134 self.betas = (
135 torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2
136 )
137 elif beta_schedule == "squaredcos_cap_v2":
138 # Glide cosine schedule
139 self.betas = betas_for_alpha_bar(num_train_timesteps)
140 else:
141 raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}")
142
143 self.alphas = 1.0 - self.betas
144 self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
145 # Currently we only support VP-type noise schedule
146 self.alpha_t = torch.sqrt(self.alphas_cumprod)
147 self.sigma_t = torch.sqrt(1 - self.alphas_cumprod)
148 self.lambda_t = torch.log(self.alpha_t) - torch.log(self.sigma_t)
149
150 # standard deviation of the initial noise distribution
151 self.init_noise_sigma = 1.0
152
153 # settings for DEIS
154 if algorithm_type not in ["deis"]:
155 if algorithm_type in ["dpmsolver", "dpmsolver++"]:
156 algorithm_type = "deis"
157 else:
158 raise NotImplementedError(f"{algorithm_type} does is not implemented for {self.__class__}")
159
160 if solver_type not in ["logrho"]:
161 if solver_type in ["midpoint", "heun"]:
162 solver_type = "logrho"
163 else:
164 raise NotImplementedError(f"solver type {solver_type} does is not implemented for {self.__class__}")
165
166 # setable values
167 self.num_inference_steps = None
168 timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=np.float32)[::-1].copy()
169 self.timesteps = torch.from_numpy(timesteps)
170 self.model_outputs = [None] * solver_order
171 self.lower_order_nums = 0
172
173 def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
174 """
175 Sets the timesteps used for the diffusion chain. Supporting function to be run before inference.
176
177 Args:
178 num_inference_steps (`int`):
179 the number of diffusion steps used when generating samples with a pre-trained model.
180 device (`str` or `torch.device`, optional):
181 the device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
182 """
183 self.num_inference_steps = num_inference_steps
184 timesteps = (
185 np.linspace(0, self.num_train_timesteps - 1, num_inference_steps + 1)
186 .round()[::-1][:-1]
187 .copy()
188 .astype(np.int64)
189 )
190 self.timesteps = torch.from_numpy(timesteps).to(device)
191 self.model_outputs = [
192 None,
193 ] * self.config.solver_order
194 self.lower_order_nums = 0
195
196 def convert_model_output(
197 self, model_output: torch.FloatTensor, timestep: int, sample: torch.FloatTensor
198 ) -> torch.FloatTensor:
199 """
200 Convert the model output to the corresponding type that the algorithm DEIS needs.
201
202 Args:
203 model_output (`torch.FloatTensor`): direct output from learned diffusion model.
204 timestep (`int`): current discrete timestep in the diffusion chain.
205 sample (`torch.FloatTensor`):
206 current instance of sample being created by diffusion process.
207
208 Returns:
209 `torch.FloatTensor`: the converted model output.
210 """
211 if self.config.prediction_type == "epsilon":
212 alpha_t, sigma_t = self.alpha_t[timestep], self.sigma_t[timestep]
213 x0_pred = (sample - sigma_t * model_output) / alpha_t
214 elif self.config.prediction_type == "sample":
215 x0_pred = model_output
216 elif self.config.prediction_type == "v_prediction":
217 alpha_t, sigma_t = self.alpha_t[timestep], self.sigma_t[timestep]
218 x0_pred = alpha_t * sample - sigma_t * model_output
219 else:
220 raise ValueError(
221 f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
222 " `v_prediction` for the DEISMultistepScheduler."
223 )
224
225 if self.config.thresholding:
226 # Dynamic thresholding in https://arxiv.org/abs/2205.11487
227 orig_dtype = x0_pred.dtype
228 if orig_dtype not in [torch.float, torch.double]:
229 x0_pred = x0_pred.float()
230 dynamic_max_val = torch.quantile(
231 torch.abs(x0_pred).reshape((x0_pred.shape[0], -1)), self.config.dynamic_thresholding_ratio, dim=1
232 )
233 dynamic_max_val = torch.maximum(
234 dynamic_max_val,
235 self.config.sample_max_value * torch.ones_like(dynamic_max_val).to(dynamic_max_val.device),
236 )[(...,) + (None,) * (x0_pred.ndim - 1)]
237 x0_pred = torch.clamp(x0_pred, -dynamic_max_val, dynamic_max_val) / dynamic_max_val
238 x0_pred = x0_pred.type(orig_dtype)
239
240 if self.config.algorithm_type == "deis":
241 alpha_t, sigma_t = self.alpha_t[timestep], self.sigma_t[timestep]
242 return (sample - alpha_t * x0_pred) / sigma_t
243 else:
244 raise NotImplementedError("only support log-rho multistep deis now")
245
246 def deis_first_order_update(
247 self,
248 model_output: torch.FloatTensor,
249 timestep: int,
250 prev_timestep: int,
251 sample: torch.FloatTensor,
252 ) -> torch.FloatTensor:
253 """
254 One step for the first-order DEIS (equivalent to DDIM).
255
256 Args:
257 model_output (`torch.FloatTensor`): direct output from learned diffusion model.
258 timestep (`int`): current discrete timestep in the diffusion chain.
259 prev_timestep (`int`): previous discrete timestep in the diffusion chain.
260 sample (`torch.FloatTensor`):
261 current instance of sample being created by diffusion process.
262
263 Returns:
264 `torch.FloatTensor`: the sample tensor at the previous timestep.
265 """
266 lambda_t, lambda_s = self.lambda_t[prev_timestep], self.lambda_t[timestep]
267 alpha_t, alpha_s = self.alpha_t[prev_timestep], self.alpha_t[timestep]
268 sigma_t, _ = self.sigma_t[prev_timestep], self.sigma_t[timestep]
269 h = lambda_t - lambda_s
270 if self.config.algorithm_type == "deis":
271 x_t = (alpha_t / alpha_s) * sample - (sigma_t * (torch.exp(h) - 1.0)) * model_output
272 else:
273 raise NotImplementedError("only support log-rho multistep deis now")
274 return x_t
275
276 def multistep_deis_second_order_update(
277 self,
278 model_output_list: List[torch.FloatTensor],
279 timestep_list: List[int],
280 prev_timestep: int,
281 sample: torch.FloatTensor,
282 ) -> torch.FloatTensor:
283 """
284 One step for the second-order multistep DEIS.
285
286 Args:
287 model_output_list (`List[torch.FloatTensor]`):
288 direct outputs from learned diffusion model at current and latter timesteps.
289 timestep (`int`): current and latter discrete timestep in the diffusion chain.
290 prev_timestep (`int`): previous discrete timestep in the diffusion chain.
291 sample (`torch.FloatTensor`):
292 current instance of sample being created by diffusion process.
293
294 Returns:
295 `torch.FloatTensor`: the sample tensor at the previous timestep.
296 """
297 t, s0, s1 = prev_timestep, timestep_list[-1], timestep_list[-2]
298 m0, m1 = model_output_list[-1], model_output_list[-2]
299 alpha_t, alpha_s0, alpha_s1 = self.alpha_t[t], self.alpha_t[s0], self.alpha_t[s1]
300 sigma_t, sigma_s0, sigma_s1 = self.sigma_t[t], self.sigma_t[s0], self.sigma_t[s1]
301
302 rho_t, rho_s0, rho_s1 = sigma_t / alpha_t, sigma_s0 / alpha_s0, sigma_s1 / alpha_s1
303
304 if self.config.algorithm_type == "deis":
305
306 def ind_fn(t, b, c):
307 # Integrate[(log(t) - log(c)) / (log(b) - log(c)), {t}]
308 return t * (-np.log(c) + np.log(t) - 1) / (np.log(b) - np.log(c))
309
310 coef1 = ind_fn(rho_t, rho_s0, rho_s1) - ind_fn(rho_s0, rho_s0, rho_s1)
311 coef2 = ind_fn(rho_t, rho_s1, rho_s0) - ind_fn(rho_s0, rho_s1, rho_s0)
312
313 x_t = alpha_t * (sample / alpha_s0 + coef1 * m0 + coef2 * m1)
314 return x_t
315 else:
316 raise NotImplementedError("only support log-rho multistep deis now")
317
318 def multistep_deis_third_order_update(
319 self,
320 model_output_list: List[torch.FloatTensor],
321 timestep_list: List[int],
322 prev_timestep: int,
323 sample: torch.FloatTensor,
324 ) -> torch.FloatTensor:
325 """
326 One step for the third-order multistep DEIS.
327
328 Args:
329 model_output_list (`List[torch.FloatTensor]`):
330 direct outputs from learned diffusion model at current and latter timesteps.
331 timestep (`int`): current and latter discrete timestep in the diffusion chain.
332 prev_timestep (`int`): previous discrete timestep in the diffusion chain.
333 sample (`torch.FloatTensor`):
334 current instance of sample being created by diffusion process.
335
336 Returns:
337 `torch.FloatTensor`: the sample tensor at the previous timestep.
338 """
339 t, s0, s1, s2 = prev_timestep, timestep_list[-1], timestep_list[-2], timestep_list[-3]
340 m0, m1, m2 = model_output_list[-1], model_output_list[-2], model_output_list[-3]
341 alpha_t, alpha_s0, alpha_s1, alpha_s2 = self.alpha_t[t], self.alpha_t[s0], self.alpha_t[s1], self.alpha_t[s2]
342 sigma_t, sigma_s0, sigma_s1, simga_s2 = self.sigma_t[t], self.sigma_t[s0], self.sigma_t[s1], self.sigma_t[s2]
343 rho_t, rho_s0, rho_s1, rho_s2 = (
344 sigma_t / alpha_t,
345 sigma_s0 / alpha_s0,
346 sigma_s1 / alpha_s1,
347 simga_s2 / alpha_s2,
348 )
349
350 if self.config.algorithm_type == "deis":
351
352 def ind_fn(t, b, c, d):
353 # Integrate[(log(t) - log(c))(log(t) - log(d)) / (log(b) - log(c))(log(b) - log(d)), {t}]
354 numerator = t * (
355 np.log(c) * (np.log(d) - np.log(t) + 1)
356 - np.log(d) * np.log(t)
357 + np.log(d)
358 + np.log(t) ** 2
359 - 2 * np.log(t)
360 + 2
361 )
362 denominator = (np.log(b) - np.log(c)) * (np.log(b) - np.log(d))
363 return numerator / denominator
364
365 coef1 = ind_fn(rho_t, rho_s0, rho_s1, rho_s2) - ind_fn(rho_s0, rho_s0, rho_s1, rho_s2)
366 coef2 = ind_fn(rho_t, rho_s1, rho_s2, rho_s0) - ind_fn(rho_s0, rho_s1, rho_s2, rho_s0)
367 coef3 = ind_fn(rho_t, rho_s2, rho_s0, rho_s1) - ind_fn(rho_s0, rho_s2, rho_s0, rho_s1)
368
369 x_t = alpha_t * (sample / alpha_s0 + coef1 * m0 + coef2 * m1 + coef3 * m2)
370
371 return x_t
372 else:
373 raise NotImplementedError("only support log-rho multistep deis now")
374
375 def step(
376 self,
377 model_output: torch.FloatTensor,
378 timestep: int,
379 sample: torch.FloatTensor,
380 return_dict: bool = True,
381 ) -> Union[SchedulerOutput, Tuple]:
382 """
383 Step function propagating the sample with the multistep DEIS.
384
385 Args:
386 model_output (`torch.FloatTensor`): direct output from learned diffusion model.
387 timestep (`int`): current discrete timestep in the diffusion chain.
388 sample (`torch.FloatTensor`):
389 current instance of sample being created by diffusion process.
390 return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
391
392 Returns:
393 [`~scheduling_utils.SchedulerOutput`] or `tuple`: [`~scheduling_utils.SchedulerOutput`] if `return_dict` is
394 True, otherwise a `tuple`. When returning a tuple, the first element is the sample tensor.
395
396 """
397 if self.num_inference_steps is None:
398 raise ValueError(
399 "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
400 )
401
402 if isinstance(timestep, torch.Tensor):
403 timestep = timestep.to(self.timesteps.device)
404 step_index = (self.timesteps == timestep).nonzero()
405 if len(step_index) == 0:
406 step_index = len(self.timesteps) - 1
407 else:
408 step_index = step_index.item()
409 prev_timestep = 0 if step_index == len(self.timesteps) - 1 else self.timesteps[step_index + 1]
410 lower_order_final = (
411 (step_index == len(self.timesteps) - 1) and self.config.lower_order_final and len(self.timesteps) < 15
412 )
413 lower_order_second = (
414 (step_index == len(self.timesteps) - 2) and self.config.lower_order_final and len(self.timesteps) < 15
415 )
416
417 model_output = self.convert_model_output(model_output, timestep, sample)
418 for i in range(self.config.solver_order - 1):
419 self.model_outputs[i] = self.model_outputs[i + 1]
420 self.model_outputs[-1] = model_output
421
422 if self.config.solver_order == 1 or self.lower_order_nums < 1 or lower_order_final:
423 prev_sample = self.deis_first_order_update(model_output, timestep, prev_timestep, sample)
424 elif self.config.solver_order == 2 or self.lower_order_nums < 2 or lower_order_second:
425 timestep_list = [self.timesteps[step_index - 1], timestep]
426 prev_sample = self.multistep_deis_second_order_update(
427 self.model_outputs, timestep_list, prev_timestep, sample
428 )
429 else:
430 timestep_list = [self.timesteps[step_index - 2], self.timesteps[step_index - 1], timestep]
431 prev_sample = self.multistep_deis_third_order_update(
432 self.model_outputs, timestep_list, prev_timestep, sample
433 )
434
435 if self.lower_order_nums < self.config.solver_order:
436 self.lower_order_nums += 1
437
438 if not return_dict:
439 return (prev_sample,)
440
441 return SchedulerOutput(prev_sample=prev_sample)
442
443 def scale_model_input(self, sample: torch.FloatTensor, *args, **kwargs) -> torch.FloatTensor:
444 """
445 Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
446 current timestep.
447
448 Args:
449 sample (`torch.FloatTensor`): input sample
450
451 Returns:
452 `torch.FloatTensor`: scaled input sample
453 """
454 return sample
455
456 def add_noise(
457 self,
458 original_samples: torch.FloatTensor,
459 noise: torch.FloatTensor,
460 timesteps: torch.IntTensor,
461 ) -> torch.FloatTensor:
462 # Make sure alphas_cumprod and timestep have same device and dtype as original_samples
463 self.alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device, dtype=original_samples.dtype)
464 timesteps = timesteps.to(original_samples.device)
465
466 sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5
467 sqrt_alpha_prod = sqrt_alpha_prod.flatten()
468 while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
469 sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)
470
471 sqrt_one_minus_alpha_prod = (1 - self.alphas_cumprod[timesteps]) ** 0.5
472 sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
473 while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape):
474 sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)
475
476 noisy_samples = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
477 return noisy_samples
478
479 def get_velocity(
480 self, sample: torch.FloatTensor, noise: torch.FloatTensor, timesteps: torch.IntTensor
481 ) -> torch.FloatTensor:
482 # Make sure alphas_cumprod and timestep have same device and dtype as sample
483 self.alphas_cumprod = self.alphas_cumprod.to(device=sample.device, dtype=sample.dtype)
484 timesteps = timesteps.to(sample.device)
485
486 sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5
487 sqrt_alpha_prod = sqrt_alpha_prod.flatten()
488 while len(sqrt_alpha_prod.shape) < len(sample.shape):
489 sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)
490
491 sqrt_one_minus_alpha_prod = (1 - self.alphas_cumprod[timesteps]) ** 0.5
492 sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
493 while len(sqrt_one_minus_alpha_prod.shape) < len(sample.shape):
494 sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)
495
496 velocity = sqrt_alpha_prod * noise - sqrt_one_minus_alpha_prod * sample
497 return velocity
498
499 def __len__(self):
500 return self.config.num_train_timesteps
generated by cgit v1.2.3-70-g09d2 (git 2.47.0) at 2024-12-23 16:43:19 +0000