scheduling_unipc_multistep.py 34.3 KB
Newer Older
Patrick von Platen's avatar
Patrick von Platen committed
1
# Copyright 2023 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
64
        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:
        raise ValueError(f"Unsupported alpha_tranform_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
74
75
    return torch.tensor(betas, dtype=torch.float32)


class UniPCMultistepScheduler(SchedulerMixin, ConfigMixin):
    """
76
    `UniPCMultistepScheduler` is a training-free framework designed for the fast sampling of diffusion models.
77

78
79
    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.
80
81

    Args:
82
83
84
85
86
87
88
89
        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
90
            `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
91
92
        trained_betas (`np.ndarray`, *optional*):
            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
93
        solver_order (`int`, default `2`):
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
            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.
110
        solver_type (`str`, default `bh2`):
111
            Solver type for UniPC. It is recommended to use `bh1` for unconditional sampling when steps < 10, and `bh2`
112
113
            otherwise.
        lower_order_final (`bool`, default `True`):
114
115
            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.
116
        disable_corrector (`list`, default `[]`):
117
118
119
            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.
120
        solver_p (`SchedulerMixin`, default `None`):
121
            Any other scheduler that if specified, the algorithm becomes `solver_p + UniC`.
122
        use_karras_sigmas (`bool`, *optional*, defaults to `False`):
123
124
125
126
127
128
129
130
131
            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):
            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.
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
    """

    _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
151
        solver_type: str = "bh2",
152
153
154
        lower_order_final: bool = True,
        disable_corrector: List[int] = [],
        solver_p: SchedulerMixin = None,
155
        use_karras_sigmas: Optional[bool] = False,
156
157
        timestep_spacing: str = "linspace",
        steps_offset: int = 0,
158
159
160
161
162
163
164
    ):
        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.
165
            self.betas = torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
        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__}")

        self.alphas = 1.0 - self.betas
        self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
        # 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)

        # 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"]:
184
                self.register_to_config(solver_type="bh2")
185
186
187
188
189
190
191
192
193
194
195
196
197
198
            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
199
200
201
202
203
204
205
206
        self._step_index = None

    @property
    def step_index(self):
        """
        The index counter for current timestep. It will increae 1 after each scheduler step.
        """
        return self._step_index
207
208
209

    def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
        """
210
        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
211
212
213

        Args:
            num_inference_steps (`int`):
214
215
216
                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.
217
        """
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
        # "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'."
            )
242

243
244
245
        sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
        if self.config.use_karras_sigmas:
            log_sigmas = np.log(sigmas)
246
            sigmas = np.flip(sigmas).copy()
247
248
            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()
249
250
251
252
253
            sigmas = np.concatenate([sigmas, sigmas[-1:]]).astype(np.float32)
        else:
            sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
            sigma_last = ((1 - self.alphas_cumprod[0]) / self.alphas_cumprod[0]) ** 0.5
            sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
254

255
256
        self.sigmas = torch.from_numpy(sigmas)
        self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.int64)
257
258
259

        self.num_inference_steps = len(timesteps)

260
261
262
263
264
265
        self.model_outputs = [
            None,
        ] * self.config.solver_order
        self.lower_order_nums = 0
        self.last_sample = None
        if self.solver_p:
266
            self.solver_p.set_timesteps(self.num_inference_steps, device=device)
267

268
269
270
        # add an index counter for schedulers that allow duplicated timesteps
        self._step_index = None

271
272
    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler._threshold_sample
    def _threshold_sample(self, sample: torch.FloatTensor) -> torch.FloatTensor:
273
274
275
276
277
278
279
280
281
282
        """
        "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
283
        batch_size, channels, *remaining_dims = sample.shape
284
285
286
287
288

        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
289
        sample = sample.reshape(batch_size, channels * np.prod(remaining_dims))
290
291
292
293
294
295
296
297
298
299

        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"

300
        sample = sample.reshape(batch_size, channels, *remaining_dims)
301
302
303
        sample = sample.to(dtype)

        return sample
304

305
306
307
    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
    def _sigma_to_t(self, sigma, log_sigmas):
        # get log sigma
308
        log_sigma = np.log(np.maximum(sigma, 1e-10))
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328

        # 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

329
330
331
332
333
334
335
    # 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

336
337
338
339
340
341
342
343
344
345
346
347
348
349
    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
    def _convert_to_karras(self, in_sigmas: torch.FloatTensor, num_inference_steps) -> torch.FloatTensor:
        """Constructs the noise schedule of Karras et al. (2022)."""

        sigma_min: float = in_sigmas[-1].item()
        sigma_max: float = in_sigmas[0].item()

        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

350
    def convert_model_output(
351
352
353
354
355
        self,
        model_output: torch.FloatTensor,
        *args,
        sample: torch.FloatTensor = None,
        **kwargs,
356
357
    ) -> torch.FloatTensor:
        r"""
358
        Convert the model output to the corresponding type the UniPC algorithm needs.
359
360

        Args:
361
362
363
364
            model_output (`torch.FloatTensor`):
                The direct output from the learned diffusion model.
            timestep (`int`):
                The current discrete timestep in the diffusion chain.
365
            sample (`torch.FloatTensor`):
366
                A current instance of a sample created by the diffusion process.
367
368

        Returns:
369
370
            `torch.FloatTensor`:
                The converted model output.
371
        """
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
        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)

388
389
390
391
392
393
394
395
396
397
        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
398
                    " `v_prediction` for the UniPCMultistepScheduler."
399
400
401
                )

            if self.config.thresholding:
402
403
                x0_pred = self._threshold_sample(x0_pred)

404
405
406
407
408
409
410
411
412
413
414
415
416
            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
417
                    " `v_prediction` for the UniPCMultistepScheduler."
418
419
420
421
422
                )

    def multistep_uni_p_bh_update(
        self,
        model_output: torch.FloatTensor,
423
424
425
426
        *args,
        sample: torch.FloatTensor = None,
        order: int = None,
        **kwargs,
427
428
429
430
431
432
    ) -> torch.FloatTensor:
        """
        One step for the UniP (B(h) version). Alternatively, `self.solver_p` is used if is specified.

        Args:
            model_output (`torch.FloatTensor`):
433
434
435
                The direct output from the learned diffusion model at the current timestep.
            prev_timestep (`int`):
                The previous discrete timestep in the diffusion chain.
436
            sample (`torch.FloatTensor`):
437
438
439
                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).
440
441

        Returns:
442
443
            `torch.FloatTensor`:
                The sample tensor at the previous timestep.
444
        """
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
        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`",
            )
462
463
        model_output_list = self.model_outputs

464
        s0 = self.timestep_list[-1]
465
466
467
468
469
470
471
        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

472
473
474
475
476
477
        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)
478
479
480
481
482
483
484

        h = lambda_t - lambda_s0
        device = sample.device

        rks = []
        D1s = []
        for i in range(1, order):
485
            si = self.step_index - i
486
            mi = model_output_list[-(i + 1)]
487
488
            alpha_si, sigma_si = self._sigma_to_alpha_sigma_t(self.sigmas[si])
            lambda_si = torch.log(alpha_si) - torch.log(sigma_si)
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
            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:
                rhos_p = torch.linalg.solve(R[:-1, :-1], b[:-1])
        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:
534
                pred_res = torch.einsum("k,bkc...->bc...", rhos_p, D1s)
535
536
537
538
539
540
            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:
541
                pred_res = torch.einsum("k,bkc...->bc...", rhos_p, D1s)
542
543
544
545
546
547
548
549
550
551
            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,
        this_model_output: torch.FloatTensor,
552
553
554
555
556
        *args,
        last_sample: torch.FloatTensor = None,
        this_sample: torch.FloatTensor = None,
        order: int = None,
        **kwargs,
557
558
559
560
561
    ) -> torch.FloatTensor:
        """
        One step for the UniC (B(h) version).

        Args:
562
563
564
565
566
567
568
569
570
571
            this_model_output (`torch.FloatTensor`):
                The model outputs at `x_t`.
            this_timestep (`int`):
                The current timestep `t`.
            last_sample (`torch.FloatTensor`):
                The generated sample before the last predictor `x_{t-1}`.
            this_sample (`torch.FloatTensor`):
                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`.
572
573

        Returns:
574
575
            `torch.FloatTensor`:
                The corrected sample tensor at the current timestep.
576
        """
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
        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`",
            )

600
601
602
603
604
605
606
        model_output_list = self.model_outputs

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

607
608
609
610
611
612
        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)
613
614
615
616
617
618
619

        h = lambda_t - lambda_s0
        device = this_sample.device

        rks = []
        D1s = []
        for i in range(1, order):
620
            si = self.step_index - (i + 1)
621
            mi = model_output_list[-(i + 1)]
622
623
            alpha_si, sigma_si = self._sigma_to_alpha_sigma_t(self.sigmas[si])
            lambda_si = torch.log(alpha_si) - torch.log(sigma_si)
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
            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:
            rhos_c = torch.linalg.solve(R, b)

        if self.predict_x0:
            x_t_ = sigma_t / sigma_s0 * x - alpha_t * h_phi_1 * m0
            if D1s is not None:
670
                corr_res = torch.einsum("k,bkc...->bc...", rhos_c[:-1], D1s)
671
672
673
674
675
676
677
            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:
678
                corr_res = torch.einsum("k,bkc...->bc...", rhos_c[:-1], D1s)
679
680
681
682
683
684
685
            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

686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
    def _init_step_index(self, timestep):
        if isinstance(timestep, torch.Tensor):
            timestep = timestep.to(self.timesteps.device)

        index_candidates = (self.timesteps == timestep).nonzero()

        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()

        self._step_index = step_index

705
706
707
708
709
710
711
712
    def step(
        self,
        model_output: torch.FloatTensor,
        timestep: int,
        sample: torch.FloatTensor,
        return_dict: bool = True,
    ) -> Union[SchedulerOutput, Tuple]:
        """
713
714
        Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
        the multistep UniPC.
715
716

        Args:
717
718
719
720
            model_output (`torch.FloatTensor`):
                The direct output from learned diffusion model.
            timestep (`int`):
                The current discrete timestep in the diffusion chain.
721
            sample (`torch.FloatTensor`):
722
723
724
                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`.
725
726

        Returns:
727
728
729
            [`~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.
730
731
732
733
734
735
736

        """
        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"
            )

737
738
        if self.step_index is None:
            self._init_step_index(timestep)
739
740

        use_corrector = (
741
            self.step_index > 0 and self.step_index - 1 not in self.disable_corrector and self.last_sample is not None
742
743
        )

744
        model_output_convert = self.convert_model_output(model_output, sample=sample)
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
        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:
761
            this_order = min(self.config.solver_order, len(self.timesteps) - self.step_index)
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
        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

778
779
780
        # upon completion increase step index by one
        self._step_index += 1

781
782
783
784
785
786
787
788
789
790
791
        if not return_dict:
            return (prev_sample,)

        return SchedulerOutput(prev_sample=prev_sample)

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

        Args:
792
793
            sample (`torch.FloatTensor`):
                The input sample.
794
795

        Returns:
796
797
            `torch.FloatTensor`:
                A scaled input sample.
798
799
800
        """
        return sample

801
    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.add_noise
802
803
804
805
    def add_noise(
        self,
        original_samples: torch.FloatTensor,
        noise: torch.FloatTensor,
806
        timesteps: torch.IntTensor,
807
    ) -> torch.FloatTensor:
808
809
810
811
812
813
814
815
816
        # 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)
817

818
        step_indices = [(schedule_timesteps == t).nonzero().item() for t in timesteps]
819

820
821
822
        sigma = sigmas[step_indices].flatten()
        while len(sigma.shape) < len(original_samples.shape):
            sigma = sigma.unsqueeze(-1)
823

824
825
        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
        noisy_samples = alpha_t * original_samples + sigma_t * noise
826
827
828
829
        return noisy_samples

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