scheduling_unipc_multistep.py 39.5 KB
Newer Older
1
# Copyright 2024 TSAIL Team and The HuggingFace Team. All rights reserved.
2
3
4
5
6
7
8
9
10
11
12
13
14
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

Wenliang Zhao's avatar
Wenliang Zhao committed
15
16
# DISCLAIMER: check https://arxiv.org/abs/2302.04867 and https://github.com/wl-zhao/UniPC for more info
# The codebase is modified based on https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py
17
18
19
20
21
22
23
24

import math
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
25
from ..utils import deprecate
26
27
28
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput


29
30
31
32
33
34
# Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar
def betas_for_alpha_bar(
    num_diffusion_timesteps,
    max_beta=0.999,
    alpha_transform_type="cosine",
):
35
36
37
38
39
40
41
42
43
44
45
46
    """
    Create a beta schedule that discretizes the given alpha_t_bar function, which defines the cumulative product of
    (1-beta) over time from t = [0,1].

    Contains a function alpha_bar that takes an argument t and transforms it to the cumulative product of (1-beta) up
    to that part of the diffusion process.


    Args:
        num_diffusion_timesteps (`int`): the number of betas to produce.
        max_beta (`float`): the maximum beta to use; use values lower than 1 to
                     prevent singularities.
47
48
        alpha_transform_type (`str`, *optional*, default to `cosine`): the type of noise schedule for alpha_bar.
                     Choose from `cosine` or `exp`
49
50
51
52

    Returns:
        betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
    """
53
    if alpha_transform_type == "cosine":
54

55
56
57
58
59
60
61
62
63
        def alpha_bar_fn(t):
            return math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2

    elif alpha_transform_type == "exp":

        def alpha_bar_fn(t):
            return math.exp(t * -12.0)

    else:
M. Tolga Cangöz's avatar
M. Tolga Cangöz committed
64
        raise ValueError(f"Unsupported alpha_transform_type: {alpha_transform_type}")
65
66
67
68
69

    betas = []
    for i in range(num_diffusion_timesteps):
        t1 = i / num_diffusion_timesteps
        t2 = (i + 1) / num_diffusion_timesteps
70
        betas.append(min(1 - alpha_bar_fn(t2) / alpha_bar_fn(t1), max_beta))
71
72
73
    return torch.tensor(betas, dtype=torch.float32)


74
75
76
77
78
79
80
# Copied from diffusers.schedulers.scheduling_ddim.rescale_zero_terminal_snr
def rescale_zero_terminal_snr(betas):
    """
    Rescales betas to have zero terminal SNR Based on https://arxiv.org/pdf/2305.08891.pdf (Algorithm 1)


    Args:
81
        betas (`torch.Tensor`):
82
83
84
            the betas that the scheduler is being initialized with.

    Returns:
85
        `torch.Tensor`: rescaled betas with zero terminal SNR
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
    """
    # Convert betas to alphas_bar_sqrt
    alphas = 1.0 - betas
    alphas_cumprod = torch.cumprod(alphas, dim=0)
    alphas_bar_sqrt = alphas_cumprod.sqrt()

    # Store old values.
    alphas_bar_sqrt_0 = alphas_bar_sqrt[0].clone()
    alphas_bar_sqrt_T = alphas_bar_sqrt[-1].clone()

    # Shift so the last timestep is zero.
    alphas_bar_sqrt -= alphas_bar_sqrt_T

    # Scale so the first timestep is back to the old value.
    alphas_bar_sqrt *= alphas_bar_sqrt_0 / (alphas_bar_sqrt_0 - alphas_bar_sqrt_T)

    # Convert alphas_bar_sqrt to betas
    alphas_bar = alphas_bar_sqrt**2  # Revert sqrt
    alphas = alphas_bar[1:] / alphas_bar[:-1]  # Revert cumprod
    alphas = torch.cat([alphas_bar[0:1], alphas])
    betas = 1 - alphas

    return betas


111
112
class UniPCMultistepScheduler(SchedulerMixin, ConfigMixin):
    """
113
    `UniPCMultistepScheduler` is a training-free framework designed for the fast sampling of diffusion models.
114

115
116
    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.
117
118

    Args:
119
120
121
122
123
124
125
126
        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
127
            `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
128
129
        trained_betas (`np.ndarray`, *optional*):
            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
130
        solver_order (`int`, default `2`):
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
            The UniPC order which can be any positive integer. The effective order of accuracy is `solver_order + 1`
            due to the UniC. It is recommended to use `solver_order=2` for guided sampling, and `solver_order=3` for
            unconditional sampling.
        prediction_type (`str`, defaults to `epsilon`, *optional*):
            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](https://imagen.research.google/video/paper.pdf) 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` and `predict_x0=True`.
        predict_x0 (`bool`, defaults to `True`):
            Whether to use the updating algorithm on the predicted x0.
147
        solver_type (`str`, default `bh2`):
148
            Solver type for UniPC. It is recommended to use `bh1` for unconditional sampling when steps < 10, and `bh2`
149
150
            otherwise.
        lower_order_final (`bool`, default `True`):
151
152
            Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. This can
            stabilize the sampling of DPMSolver for steps < 15, especially for steps <= 10.
153
        disable_corrector (`list`, default `[]`):
154
155
156
            Decides which step to disable the corrector to mitigate the misalignment between `epsilon_theta(x_t, c)`
            and `epsilon_theta(x_t^c, c)` which can influence convergence for a large guidance scale. Corrector is
            usually disabled during the first few steps.
157
        solver_p (`SchedulerMixin`, default `None`):
158
            Any other scheduler that if specified, the algorithm becomes `solver_p + UniC`.
159
        use_karras_sigmas (`bool`, *optional*, defaults to `False`):
160
161
162
163
164
165
            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](https://huggingface.co/papers/2305.08891) for more information.
        steps_offset (`int`, defaults to 0):
166
            An offset added to the inference steps, as required by some model families.
167
        final_sigmas_type (`str`, defaults to `"zero"`):
168
169
            The final `sigma` value for the noise schedule during the sampling process. If `"sigma_min"`, the final
            sigma is the same as the last sigma in the training schedule. If `zero`, the final sigma is set to 0.
170
171
172
173
        rescale_betas_zero_snr (`bool`, defaults to `False`):
            Whether to rescale the betas to have zero terminal SNR. This enables the model to generate very bright and
            dark samples instead of limiting it to samples with medium brightness. Loosely related to
            [`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506).
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
    """

    _compatibles = [e.name for e in KarrasDiffusionSchedulers]
    order = 1

    @register_to_config
    def __init__(
        self,
        num_train_timesteps: int = 1000,
        beta_start: float = 0.0001,
        beta_end: float = 0.02,
        beta_schedule: str = "linear",
        trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
        solver_order: int = 2,
        prediction_type: str = "epsilon",
        thresholding: bool = False,
        dynamic_thresholding_ratio: float = 0.995,
        sample_max_value: float = 1.0,
        predict_x0: bool = True,
Wenliang Zhao's avatar
Wenliang Zhao committed
193
        solver_type: str = "bh2",
194
195
196
        lower_order_final: bool = True,
        disable_corrector: List[int] = [],
        solver_p: SchedulerMixin = None,
197
        use_karras_sigmas: Optional[bool] = False,
198
199
        timestep_spacing: str = "linspace",
        steps_offset: int = 0,
200
        final_sigmas_type: Optional[str] = "zero",  # "zero", "sigma_min"
201
        rescale_betas_zero_snr: bool = False,
202
203
204
205
206
207
208
    ):
        if trained_betas is not None:
            self.betas = torch.tensor(trained_betas, dtype=torch.float32)
        elif beta_schedule == "linear":
            self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32)
        elif beta_schedule == "scaled_linear":
            # this schedule is very specific to the latent diffusion model.
209
            self.betas = torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2
210
211
212
213
214
215
        elif beta_schedule == "squaredcos_cap_v2":
            # Glide cosine schedule
            self.betas = betas_for_alpha_bar(num_train_timesteps)
        else:
            raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}")

216
217
218
        if rescale_betas_zero_snr:
            self.betas = rescale_zero_terminal_snr(self.betas)

219
220
        self.alphas = 1.0 - self.betas
        self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
221
222
223
224
225
226

        if rescale_betas_zero_snr:
            # Close to 0 without being 0 so first sigma is not inf
            # FP16 smallest positive subnormal works well here
            self.alphas_cumprod[-1] = 2**-24

227
228
229
230
        # Currently we only support VP-type noise schedule
        self.alpha_t = torch.sqrt(self.alphas_cumprod)
        self.sigma_t = torch.sqrt(1 - self.alphas_cumprod)
        self.lambda_t = torch.log(self.alpha_t) - torch.log(self.sigma_t)
231
        self.sigmas = ((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5
232
233
234
235
236
237

        # standard deviation of the initial noise distribution
        self.init_noise_sigma = 1.0

        if solver_type not in ["bh1", "bh2"]:
            if solver_type in ["midpoint", "heun", "logrho"]:
238
                self.register_to_config(solver_type="bh2")
239
240
241
242
243
244
245
246
247
248
249
250
251
252
            else:
                raise NotImplementedError(f"{solver_type} does is not implemented for {self.__class__}")

        self.predict_x0 = predict_x0
        # setable values
        self.num_inference_steps = None
        timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=np.float32)[::-1].copy()
        self.timesteps = torch.from_numpy(timesteps)
        self.model_outputs = [None] * solver_order
        self.timestep_list = [None] * solver_order
        self.lower_order_nums = 0
        self.disable_corrector = disable_corrector
        self.solver_p = solver_p
        self.last_sample = None
253
        self._step_index = None
254
        self._begin_index = None
255
        self.sigmas = self.sigmas.to("cpu")  # to avoid too much CPU/GPU communication
256
257
258
259

    @property
    def step_index(self):
        """
M. Tolga Cangöz's avatar
M. Tolga Cangöz committed
260
        The index counter for current timestep. It will increase 1 after each scheduler step.
261
262
        """
        return self._step_index
263

264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
    @property
    def begin_index(self):
        """
        The index for the first timestep. It should be set from pipeline with `set_begin_index` method.
        """
        return self._begin_index

    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.set_begin_index
    def set_begin_index(self, begin_index: int = 0):
        """
        Sets the begin index for the scheduler. This function should be run from pipeline before the inference.

        Args:
            begin_index (`int`):
                The begin index for the scheduler.
        """
        self._begin_index = begin_index

282
283
    def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
        """
284
        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
285
286
287

        Args:
            num_inference_steps (`int`):
288
289
290
                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.
291
        """
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
        # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
        if self.config.timestep_spacing == "linspace":
            timesteps = (
                np.linspace(0, self.config.num_train_timesteps - 1, num_inference_steps + 1)
                .round()[::-1][:-1]
                .copy()
                .astype(np.int64)
            )
        elif self.config.timestep_spacing == "leading":
            step_ratio = self.config.num_train_timesteps // (num_inference_steps + 1)
            # creates integer timesteps by multiplying by ratio
            # casting to int to avoid issues when num_inference_step is power of 3
            timesteps = (np.arange(0, num_inference_steps + 1) * step_ratio).round()[::-1][:-1].copy().astype(np.int64)
            timesteps += self.config.steps_offset
        elif self.config.timestep_spacing == "trailing":
            step_ratio = self.config.num_train_timesteps / num_inference_steps
            # creates integer timesteps by multiplying by ratio
            # casting to int to avoid issues when num_inference_step is power of 3
            timesteps = np.arange(self.config.num_train_timesteps, 0, -step_ratio).round().copy().astype(np.int64)
            timesteps -= 1
        else:
            raise ValueError(
                f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."
            )
316

317
318
319
        sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
        if self.config.use_karras_sigmas:
            log_sigmas = np.log(sigmas)
320
            sigmas = np.flip(sigmas).copy()
321
322
            sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
            timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]).round()
323
324
325
326
327
328
329
330
331
            if self.config.final_sigmas_type == "sigma_min":
                sigma_last = sigmas[-1]
            elif self.config.final_sigmas_type == "zero":
                sigma_last = 0
            else:
                raise ValueError(
                    f"`final_sigmas_type` must be one of 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}"
                )
            sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
332
333
        else:
            sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
334
335
336
337
338
339
340
341
            if self.config.final_sigmas_type == "sigma_min":
                sigma_last = ((1 - self.alphas_cumprod[0]) / self.alphas_cumprod[0]) ** 0.5
            elif self.config.final_sigmas_type == "zero":
                sigma_last = 0
            else:
                raise ValueError(
                    f"`final_sigmas_type` must be one of 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}"
                )
342
            sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
343

344
345
        self.sigmas = torch.from_numpy(sigmas)
        self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.int64)
346
347
348

        self.num_inference_steps = len(timesteps)

349
350
351
352
353
354
        self.model_outputs = [
            None,
        ] * self.config.solver_order
        self.lower_order_nums = 0
        self.last_sample = None
        if self.solver_p:
355
            self.solver_p.set_timesteps(self.num_inference_steps, device=device)
356

357
358
        # add an index counter for schedulers that allow duplicated timesteps
        self._step_index = None
359
        self._begin_index = None
360
        self.sigmas = self.sigmas.to("cpu")  # to avoid too much CPU/GPU communication
361

362
    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler._threshold_sample
363
    def _threshold_sample(self, sample: torch.Tensor) -> torch.Tensor:
364
365
366
367
368
369
370
371
372
373
        """
        "Dynamic thresholding: At each sampling step we set s to a certain percentile absolute pixel value in xt0 (the
        prediction of x_0 at timestep t), and if s > 1, then we threshold xt0 to the range [-s, s] and then divide by
        s. Dynamic thresholding pushes saturated pixels (those near -1 and 1) inwards, thereby actively preventing
        pixels from saturation at each step. We find that dynamic thresholding results in significantly better
        photorealism as well as better image-text alignment, especially when using very large guidance weights."

        https://arxiv.org/abs/2205.11487
        """
        dtype = sample.dtype
374
        batch_size, channels, *remaining_dims = sample.shape
375
376
377
378
379

        if dtype not in (torch.float32, torch.float64):
            sample = sample.float()  # upcast for quantile calculation, and clamp not implemented for cpu half

        # Flatten sample for doing quantile calculation along each image
380
        sample = sample.reshape(batch_size, channels * np.prod(remaining_dims))
381
382
383
384
385
386
387
388
389
390

        abs_sample = sample.abs()  # "a certain percentile absolute pixel value"

        s = torch.quantile(abs_sample, self.config.dynamic_thresholding_ratio, dim=1)
        s = torch.clamp(
            s, min=1, max=self.config.sample_max_value
        )  # When clamped to min=1, equivalent to standard clipping to [-1, 1]
        s = s.unsqueeze(1)  # (batch_size, 1) because clamp will broadcast along dim=0
        sample = torch.clamp(sample, -s, s) / s  # "we threshold xt0 to the range [-s, s] and then divide by s"

391
        sample = sample.reshape(batch_size, channels, *remaining_dims)
392
393
394
        sample = sample.to(dtype)

        return sample
395

396
397
398
    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
    def _sigma_to_t(self, sigma, log_sigmas):
        # get log sigma
399
        log_sigma = np.log(np.maximum(sigma, 1e-10))
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419

        # get distribution
        dists = log_sigma - log_sigmas[:, np.newaxis]

        # get sigmas range
        low_idx = np.cumsum((dists >= 0), axis=0).argmax(axis=0).clip(max=log_sigmas.shape[0] - 2)
        high_idx = low_idx + 1

        low = log_sigmas[low_idx]
        high = log_sigmas[high_idx]

        # interpolate sigmas
        w = (low - log_sigma) / (low - high)
        w = np.clip(w, 0, 1)

        # transform interpolation to time range
        t = (1 - w) * low_idx + w * high_idx
        t = t.reshape(sigma.shape)
        return t

420
421
422
423
424
425
426
    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._sigma_to_alpha_sigma_t
    def _sigma_to_alpha_sigma_t(self, sigma):
        alpha_t = 1 / ((sigma**2 + 1) ** 0.5)
        sigma_t = sigma * alpha_t

        return alpha_t, sigma_t

427
    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
428
    def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
429
430
        """Constructs the noise schedule of Karras et al. (2022)."""

Suraj Patil's avatar
Suraj Patil committed
431
432
433
434
435
436
437
438
439
440
441
442
443
444
        # Hack to make sure that other schedulers which copy this function don't break
        # TODO: Add this logic to the other schedulers
        if hasattr(self.config, "sigma_min"):
            sigma_min = self.config.sigma_min
        else:
            sigma_min = None

        if hasattr(self.config, "sigma_max"):
            sigma_max = self.config.sigma_max
        else:
            sigma_max = None

        sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
        sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()
445
446
447
448
449
450
451
452

        rho = 7.0  # 7.0 is the value used in the paper
        ramp = np.linspace(0, 1, num_inference_steps)
        min_inv_rho = sigma_min ** (1 / rho)
        max_inv_rho = sigma_max ** (1 / rho)
        sigmas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
        return sigmas

453
    def convert_model_output(
454
        self,
455
        model_output: torch.Tensor,
456
        *args,
457
        sample: torch.Tensor = None,
458
        **kwargs,
459
    ) -> torch.Tensor:
460
        r"""
461
        Convert the model output to the corresponding type the UniPC algorithm needs.
462
463

        Args:
464
            model_output (`torch.Tensor`):
465
466
467
                The direct output from the learned diffusion model.
            timestep (`int`):
                The current discrete timestep in the diffusion chain.
468
            sample (`torch.Tensor`):
469
                A current instance of a sample created by the diffusion process.
470
471

        Returns:
472
            `torch.Tensor`:
473
                The converted model output.
474
        """
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
        timestep = args[0] if len(args) > 0 else kwargs.pop("timestep", None)
        if sample is None:
            if len(args) > 1:
                sample = args[1]
            else:
                raise ValueError("missing `sample` as a required keyward argument")
        if timestep is not None:
            deprecate(
                "timesteps",
                "1.0.0",
                "Passing `timesteps` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
            )

        sigma = self.sigmas[self.step_index]
        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)

491
492
493
494
495
496
497
498
499
500
        if self.predict_x0:
            if self.config.prediction_type == "epsilon":
                x0_pred = (sample - sigma_t * model_output) / alpha_t
            elif self.config.prediction_type == "sample":
                x0_pred = model_output
            elif self.config.prediction_type == "v_prediction":
                x0_pred = alpha_t * sample - sigma_t * model_output
            else:
                raise ValueError(
                    f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
Wenliang Zhao's avatar
Wenliang Zhao committed
501
                    " `v_prediction` for the UniPCMultistepScheduler."
502
503
504
                )

            if self.config.thresholding:
505
506
                x0_pred = self._threshold_sample(x0_pred)

507
508
509
510
511
512
513
514
515
516
517
518
519
            return x0_pred
        else:
            if self.config.prediction_type == "epsilon":
                return model_output
            elif self.config.prediction_type == "sample":
                epsilon = (sample - alpha_t * model_output) / sigma_t
                return epsilon
            elif self.config.prediction_type == "v_prediction":
                epsilon = alpha_t * model_output + sigma_t * sample
                return epsilon
            else:
                raise ValueError(
                    f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
Wenliang Zhao's avatar
Wenliang Zhao committed
520
                    " `v_prediction` for the UniPCMultistepScheduler."
521
522
523
524
                )

    def multistep_uni_p_bh_update(
        self,
525
        model_output: torch.Tensor,
526
        *args,
527
        sample: torch.Tensor = None,
528
529
        order: int = None,
        **kwargs,
530
    ) -> torch.Tensor:
531
532
533
534
        """
        One step for the UniP (B(h) version). Alternatively, `self.solver_p` is used if is specified.

        Args:
535
            model_output (`torch.Tensor`):
536
537
538
                The direct output from the learned diffusion model at the current timestep.
            prev_timestep (`int`):
                The previous discrete timestep in the diffusion chain.
539
            sample (`torch.Tensor`):
540
541
542
                A current instance of a sample created by the diffusion process.
            order (`int`):
                The order of UniP at this timestep (corresponds to the *p* in UniPC-p).
543
544

        Returns:
545
            `torch.Tensor`:
546
                The sample tensor at the previous timestep.
547
        """
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
        prev_timestep = args[0] if len(args) > 0 else kwargs.pop("prev_timestep", None)
        if sample is None:
            if len(args) > 1:
                sample = args[1]
            else:
                raise ValueError(" missing `sample` as a required keyward argument")
        if order is None:
            if len(args) > 2:
                order = args[2]
            else:
                raise ValueError(" missing `order` as a required keyward argument")
        if prev_timestep is not None:
            deprecate(
                "prev_timestep",
                "1.0.0",
                "Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
            )
565
566
        model_output_list = self.model_outputs

567
        s0 = self.timestep_list[-1]
568
569
570
571
572
573
574
        m0 = model_output_list[-1]
        x = sample

        if self.solver_p:
            x_t = self.solver_p.step(model_output, s0, x).prev_sample
            return x_t

575
576
577
578
579
580
        sigma_t, sigma_s0 = self.sigmas[self.step_index + 1], self.sigmas[self.step_index]
        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
        alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)

        lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
        lambda_s0 = torch.log(alpha_s0) - torch.log(sigma_s0)
581
582
583
584
585
586
587

        h = lambda_t - lambda_s0
        device = sample.device

        rks = []
        D1s = []
        for i in range(1, order):
588
            si = self.step_index - i
589
            mi = model_output_list[-(i + 1)]
590
591
            alpha_si, sigma_si = self._sigma_to_alpha_sigma_t(self.sigmas[si])
            lambda_si = torch.log(alpha_si) - torch.log(sigma_si)
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
            rk = (lambda_si - lambda_s0) / h
            rks.append(rk)
            D1s.append((mi - m0) / rk)

        rks.append(1.0)
        rks = torch.tensor(rks, device=device)

        R = []
        b = []

        hh = -h if self.predict_x0 else h
        h_phi_1 = torch.expm1(hh)  # h\phi_1(h) = e^h - 1
        h_phi_k = h_phi_1 / hh - 1

        factorial_i = 1

        if self.config.solver_type == "bh1":
            B_h = hh
        elif self.config.solver_type == "bh2":
            B_h = torch.expm1(hh)
        else:
            raise NotImplementedError()

        for i in range(1, order + 1):
            R.append(torch.pow(rks, i - 1))
            b.append(h_phi_k * factorial_i / B_h)
            factorial_i *= i + 1
            h_phi_k = h_phi_k / hh - 1 / factorial_i

        R = torch.stack(R)
        b = torch.tensor(b, device=device)

        if len(D1s) > 0:
            D1s = torch.stack(D1s, dim=1)  # (B, K)
            # for order 2, we use a simplified version
            if order == 2:
                rhos_p = torch.tensor([0.5], dtype=x.dtype, device=device)
            else:
630
                rhos_p = torch.linalg.solve(R[:-1, :-1], b[:-1]).to(device).to(x.dtype)
631
632
633
634
635
636
        else:
            D1s = None

        if self.predict_x0:
            x_t_ = sigma_t / sigma_s0 * x - alpha_t * h_phi_1 * m0
            if D1s is not None:
637
                pred_res = torch.einsum("k,bkc...->bc...", rhos_p, D1s)
638
639
640
641
642
643
            else:
                pred_res = 0
            x_t = x_t_ - alpha_t * B_h * pred_res
        else:
            x_t_ = alpha_t / alpha_s0 * x - sigma_t * h_phi_1 * m0
            if D1s is not None:
644
                pred_res = torch.einsum("k,bkc...->bc...", rhos_p, D1s)
645
646
647
648
649
650
651
652
653
            else:
                pred_res = 0
            x_t = x_t_ - sigma_t * B_h * pred_res

        x_t = x_t.to(x.dtype)
        return x_t

    def multistep_uni_c_bh_update(
        self,
654
        this_model_output: torch.Tensor,
655
        *args,
656
657
        last_sample: torch.Tensor = None,
        this_sample: torch.Tensor = None,
658
659
        order: int = None,
        **kwargs,
660
    ) -> torch.Tensor:
661
662
663
664
        """
        One step for the UniC (B(h) version).

        Args:
665
            this_model_output (`torch.Tensor`):
666
667
668
                The model outputs at `x_t`.
            this_timestep (`int`):
                The current timestep `t`.
669
            last_sample (`torch.Tensor`):
670
                The generated sample before the last predictor `x_{t-1}`.
671
            this_sample (`torch.Tensor`):
672
673
674
                The generated sample after the last predictor `x_{t}`.
            order (`int`):
                The `p` of UniC-p at this step. The effective order of accuracy should be `order + 1`.
675
676

        Returns:
677
            `torch.Tensor`:
678
                The corrected sample tensor at the current timestep.
679
        """
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
        this_timestep = args[0] if len(args) > 0 else kwargs.pop("this_timestep", None)
        if last_sample is None:
            if len(args) > 1:
                last_sample = args[1]
            else:
                raise ValueError(" missing`last_sample` as a required keyward argument")
        if this_sample is None:
            if len(args) > 2:
                this_sample = args[2]
            else:
                raise ValueError(" missing`this_sample` as a required keyward argument")
        if order is None:
            if len(args) > 3:
                order = args[3]
            else:
                raise ValueError(" missing`order` as a required keyward argument")
        if this_timestep is not None:
            deprecate(
                "this_timestep",
                "1.0.0",
                "Passing `this_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
            )

703
704
705
706
707
708
709
        model_output_list = self.model_outputs

        m0 = model_output_list[-1]
        x = last_sample
        x_t = this_sample
        model_t = this_model_output

710
711
712
713
714
715
        sigma_t, sigma_s0 = self.sigmas[self.step_index], self.sigmas[self.step_index - 1]
        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
        alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)

        lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
        lambda_s0 = torch.log(alpha_s0) - torch.log(sigma_s0)
716
717
718
719
720
721
722

        h = lambda_t - lambda_s0
        device = this_sample.device

        rks = []
        D1s = []
        for i in range(1, order):
723
            si = self.step_index - (i + 1)
724
            mi = model_output_list[-(i + 1)]
725
726
            alpha_si, sigma_si = self._sigma_to_alpha_sigma_t(self.sigmas[si])
            lambda_si = torch.log(alpha_si) - torch.log(sigma_si)
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
            rk = (lambda_si - lambda_s0) / h
            rks.append(rk)
            D1s.append((mi - m0) / rk)

        rks.append(1.0)
        rks = torch.tensor(rks, device=device)

        R = []
        b = []

        hh = -h if self.predict_x0 else h
        h_phi_1 = torch.expm1(hh)  # h\phi_1(h) = e^h - 1
        h_phi_k = h_phi_1 / hh - 1

        factorial_i = 1

        if self.config.solver_type == "bh1":
            B_h = hh
        elif self.config.solver_type == "bh2":
            B_h = torch.expm1(hh)
        else:
            raise NotImplementedError()

        for i in range(1, order + 1):
            R.append(torch.pow(rks, i - 1))
            b.append(h_phi_k * factorial_i / B_h)
            factorial_i *= i + 1
            h_phi_k = h_phi_k / hh - 1 / factorial_i

        R = torch.stack(R)
        b = torch.tensor(b, device=device)

        if len(D1s) > 0:
            D1s = torch.stack(D1s, dim=1)
        else:
            D1s = None

        # for order 1, we use a simplified version
        if order == 1:
            rhos_c = torch.tensor([0.5], dtype=x.dtype, device=device)
        else:
768
            rhos_c = torch.linalg.solve(R, b).to(device).to(x.dtype)
769
770
771
772

        if self.predict_x0:
            x_t_ = sigma_t / sigma_s0 * x - alpha_t * h_phi_1 * m0
            if D1s is not None:
773
                corr_res = torch.einsum("k,bkc...->bc...", rhos_c[:-1], D1s)
774
775
776
777
778
779
780
            else:
                corr_res = 0
            D1_t = model_t - m0
            x_t = x_t_ - alpha_t * B_h * (corr_res + rhos_c[-1] * D1_t)
        else:
            x_t_ = alpha_t / alpha_s0 * x - sigma_t * h_phi_1 * m0
            if D1s is not None:
781
                corr_res = torch.einsum("k,bkc...->bc...", rhos_c[:-1], D1s)
782
783
784
785
786
787
788
            else:
                corr_res = 0
            D1_t = model_t - m0
            x_t = x_t_ - sigma_t * B_h * (corr_res + rhos_c[-1] * D1_t)
        x_t = x_t.to(x.dtype)
        return x_t

789
790
791
792
    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.index_for_timestep
    def index_for_timestep(self, timestep, schedule_timesteps=None):
        if schedule_timesteps is None:
            schedule_timesteps = self.timesteps
793

794
        index_candidates = (schedule_timesteps == timestep).nonzero()
795
796
797
798
799
800
801
802
803
804
805
806

        if len(index_candidates) == 0:
            step_index = len(self.timesteps) - 1
        # The sigma index that is taken for the **very** first `step`
        # is always the second index (or the last index if there is only 1)
        # This way we can ensure we don't accidentally skip a sigma in
        # case we start in the middle of the denoising schedule (e.g. for image-to-image)
        elif len(index_candidates) > 1:
            step_index = index_candidates[1].item()
        else:
            step_index = index_candidates[0].item()

807
808
809
810
811
812
813
814
815
816
817
818
819
820
        return step_index

    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._init_step_index
    def _init_step_index(self, timestep):
        """
        Initialize the step_index counter for the scheduler.
        """

        if self.begin_index is None:
            if isinstance(timestep, torch.Tensor):
                timestep = timestep.to(self.timesteps.device)
            self._step_index = self.index_for_timestep(timestep)
        else:
            self._step_index = self._begin_index
821

822
823
    def step(
        self,
824
        model_output: torch.Tensor,
825
        timestep: int,
826
        sample: torch.Tensor,
827
828
829
        return_dict: bool = True,
    ) -> Union[SchedulerOutput, Tuple]:
        """
830
831
        Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
        the multistep UniPC.
832
833

        Args:
834
            model_output (`torch.Tensor`):
835
836
837
                The direct output from learned diffusion model.
            timestep (`int`):
                The current discrete timestep in the diffusion chain.
838
            sample (`torch.Tensor`):
839
840
841
                A current instance of a sample created by the diffusion process.
            return_dict (`bool`):
                Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`.
842
843

        Returns:
844
845
846
            [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
                If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a
                tuple is returned where the first element is the sample tensor.
847
848
849
850
851
852
853

        """
        if self.num_inference_steps is None:
            raise ValueError(
                "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
            )

854
855
        if self.step_index is None:
            self._init_step_index(timestep)
856
857

        use_corrector = (
858
            self.step_index > 0 and self.step_index - 1 not in self.disable_corrector and self.last_sample is not None
859
860
        )

861
        model_output_convert = self.convert_model_output(model_output, sample=sample)
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
        if use_corrector:
            sample = self.multistep_uni_c_bh_update(
                this_model_output=model_output_convert,
                last_sample=self.last_sample,
                this_sample=sample,
                order=self.this_order,
            )

        for i in range(self.config.solver_order - 1):
            self.model_outputs[i] = self.model_outputs[i + 1]
            self.timestep_list[i] = self.timestep_list[i + 1]

        self.model_outputs[-1] = model_output_convert
        self.timestep_list[-1] = timestep

        if self.config.lower_order_final:
878
            this_order = min(self.config.solver_order, len(self.timesteps) - self.step_index)
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
        else:
            this_order = self.config.solver_order

        self.this_order = min(this_order, self.lower_order_nums + 1)  # warmup for multistep
        assert self.this_order > 0

        self.last_sample = sample
        prev_sample = self.multistep_uni_p_bh_update(
            model_output=model_output,  # pass the original non-converted model output, in case solver-p is used
            sample=sample,
            order=self.this_order,
        )

        if self.lower_order_nums < self.config.solver_order:
            self.lower_order_nums += 1

895
896
897
        # upon completion increase step index by one
        self._step_index += 1

898
899
900
901
902
        if not return_dict:
            return (prev_sample,)

        return SchedulerOutput(prev_sample=prev_sample)

903
    def scale_model_input(self, sample: torch.Tensor, *args, **kwargs) -> torch.Tensor:
904
905
906
907
908
        """
        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
        current timestep.

        Args:
909
            sample (`torch.Tensor`):
910
                The input sample.
911
912

        Returns:
913
            `torch.Tensor`:
914
                A scaled input sample.
915
916
917
        """
        return sample

918
    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.add_noise
919
920
    def add_noise(
        self,
921
922
        original_samples: torch.Tensor,
        noise: torch.Tensor,
923
        timesteps: torch.IntTensor,
924
    ) -> torch.Tensor:
925
926
927
928
929
930
931
932
933
        # Make sure sigmas and timesteps have the same device and dtype as original_samples
        sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
        if original_samples.device.type == "mps" and torch.is_floating_point(timesteps):
            # mps does not support float64
            schedule_timesteps = self.timesteps.to(original_samples.device, dtype=torch.float32)
            timesteps = timesteps.to(original_samples.device, dtype=torch.float32)
        else:
            schedule_timesteps = self.timesteps.to(original_samples.device)
            timesteps = timesteps.to(original_samples.device)
934

935
        # begin_index is None when the scheduler is used for training or pipeline does not implement set_begin_index
936
937
        if self.begin_index is None:
            step_indices = [self.index_for_timestep(t, schedule_timesteps) for t in timesteps]
938
939
940
        elif self.step_index is not None:
            # add_noise is called after first denoising step (for inpainting)
            step_indices = [self.step_index] * timesteps.shape[0]
941
        else:
M. Tolga Cangöz's avatar
M. Tolga Cangöz committed
942
            # add noise is called before first denoising step to create initial latent(img2img)
943
            step_indices = [self.begin_index] * timesteps.shape[0]
944

945
946
947
        sigma = sigmas[step_indices].flatten()
        while len(sigma.shape) < len(original_samples.shape):
            sigma = sigma.unsqueeze(-1)
948

949
950
        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
        noisy_samples = alpha_t * original_samples + sigma_t * noise
951
952
953
954
        return noisy_samples

    def __len__(self):
        return self.config.num_train_timesteps