scheduling_dpmsolver_singlestep.py 40.8 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
15
16
17
18
19
20
21
22
23
#
# 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.

# DISCLAIMER: This file is strongly influenced by https://github.com/LuChengTHU/dpm-solver

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

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
24
from ..utils import deprecate, logging
Kashif Rasul's avatar
Kashif Rasul committed
25
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
26
27


Patrick von Platen's avatar
Patrick von Platen committed
28
29
30
logger = logging.get_logger(__name__)  # pylint: disable=invalid-name


31
# Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar
YiYi Xu's avatar
YiYi Xu committed
32
33
34
35
36
def betas_for_alpha_bar(
    num_diffusion_timesteps,
    max_beta=0.999,
    alpha_transform_type="cosine",
):
37
38
39
40
41
42
43
44
45
46
47
48
    """
    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.
YiYi Xu's avatar
YiYi Xu committed
49
50
        alpha_transform_type (`str`, *optional*, default to `cosine`): the type of noise schedule for alpha_bar.
                     Choose from `cosine` or `exp`
51
52
53
54

    Returns:
        betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
    """
YiYi Xu's avatar
YiYi Xu committed
55
    if alpha_transform_type == "cosine":
56

YiYi Xu's avatar
YiYi Xu committed
57
58
59
60
61
62
63
64
65
66
        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}")
67
68
69
70
71

    betas = []
    for i in range(num_diffusion_timesteps):
        t1 = i / num_diffusion_timesteps
        t2 = (i + 1) / num_diffusion_timesteps
YiYi Xu's avatar
YiYi Xu committed
72
        betas.append(min(1 - alpha_bar_fn(t2) / alpha_bar_fn(t1), max_beta))
73
74
75
76
77
    return torch.tensor(betas, dtype=torch.float32)


class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
    """
78
    `DPMSolverSinglestepScheduler` is a fast dedicated high-order solver for diffusion ODEs.
79

80
81
    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.
82
83

    Args:
84
85
86
87
88
89
90
91
        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
92
            `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
93
94
95
96
        trained_betas (`np.ndarray`, *optional*):
            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
        solver_order (`int`, defaults to 2):
            The DPMSolver order which can be `1` or `2` or `3`. It is recommended to use `solver_order=2` for guided
97
            sampling, and `solver_order=3` for unconditional sampling.
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
        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
            `algorithm_type="dpmsolver++"`.
        algorithm_type (`str`, defaults to `dpmsolver++`):
            Algorithm type for the solver; can be `dpmsolver`, `dpmsolver++`, `sde-dpmsolver` or `sde-dpmsolver++`. The
            `dpmsolver` type implements the algorithms in the [DPMSolver](https://huggingface.co/papers/2206.00927)
            paper, and the `dpmsolver++` type implements the algorithms in the
            [DPMSolver++](https://huggingface.co/papers/2211.01095) paper. It is recommended to use `dpmsolver++` or
            `sde-dpmsolver++` with `solver_order=2` for guided sampling like in Stable Diffusion.
        solver_type (`str`, defaults to `midpoint`):
            Solver type for the second-order solver; can be `midpoint` or `heun`. The solver type slightly affects the
            sample quality, especially for a small number of steps. It is recommended to use `midpoint` solvers.
        lower_order_final (`bool`, defaults to `True`):
            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.
122
        use_karras_sigmas (`bool`, *optional*, defaults to `False`):
123
124
125
126
127
            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}.
        lambda_min_clipped (`float`, defaults to `-inf`):
            Clipping threshold for the minimum value of `lambda(t)` for numerical stability. This is critical for the
            cosine (`squaredcos_cap_v2`) noise schedule.
128
        variance_type (`str`, *optional*):
129
130
            Set to "learned" or "learned_range" for diffusion models that predict variance. If set, the model's output
            contains the predicted Gaussian variance.
131
132
    """

Kashif Rasul's avatar
Kashif Rasul committed
133
    _compatibles = [e.name for e in KarrasDiffusionSchedulers]
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
    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[np.ndarray] = None,
        solver_order: int = 2,
        prediction_type: str = "epsilon",
        thresholding: bool = False,
        dynamic_thresholding_ratio: float = 0.995,
        sample_max_value: float = 1.0,
        algorithm_type: str = "dpmsolver++",
        solver_type: str = "midpoint",
        lower_order_final: bool = True,
152
        use_karras_sigmas: Optional[bool] = False,
153
154
        lambda_min_clipped: float = -float("inf"),
        variance_type: Optional[str] = None,
155
156
157
158
159
160
161
    ):
        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.
162
            self.betas = torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2
163
164
165
166
167
168
169
170
171
172
173
174
        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)
175
        self.sigmas = ((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5
176
177
178
179
180
181

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

        # settings for DPM-Solver
        if algorithm_type not in ["dpmsolver", "dpmsolver++"]:
182
            if algorithm_type == "deis":
183
                self.register_to_config(algorithm_type="dpmsolver++")
184
185
            else:
                raise NotImplementedError(f"{algorithm_type} does is not implemented for {self.__class__}")
186
        if solver_type not in ["midpoint", "heun"]:
187
            if solver_type in ["logrho", "bh1", "bh2"]:
188
                self.register_to_config(solver_type="midpoint")
189
190
            else:
                raise NotImplementedError(f"{solver_type} does is not implemented for {self.__class__}")
191
192
193
194
195
196
197
198

        # 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.sample = None
        self.order_list = self.get_order_list(num_train_timesteps)
199
        self._step_index = None
200
        self.sigmas.to("cpu")  # to avoid too much CPU/GPU communication
201
202
203
204
205
206
207

    def get_order_list(self, num_inference_steps: int) -> List[int]:
        """
        Computes the solver order at each time step.

        Args:
            num_inference_steps (`int`):
208
                The number of diffusion steps used when generating samples with a pre-trained model.
209
210
        """
        steps = num_inference_steps
211
212
        order = self.config.solver_order
        if self.config.lower_order_final:
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
            if order == 3:
                if steps % 3 == 0:
                    orders = [1, 2, 3] * (steps // 3 - 1) + [1, 2] + [1]
                elif steps % 3 == 1:
                    orders = [1, 2, 3] * (steps // 3) + [1]
                else:
                    orders = [1, 2, 3] * (steps // 3) + [1, 2]
            elif order == 2:
                if steps % 2 == 0:
                    orders = [1, 2] * (steps // 2)
                else:
                    orders = [1, 2] * (steps // 2) + [1]
            elif order == 1:
                orders = [1] * steps
        else:
            if order == 3:
                orders = [1, 2, 3] * (steps // 3)
            elif order == 2:
                orders = [1, 2] * (steps // 2)
            elif order == 1:
                orders = [1] * steps
        return orders

236
237
238
239
240
241
242
    @property
    def step_index(self):
        """
        The index counter for current timestep. It will increae 1 after each scheduler step.
        """
        return self._step_index

243
244
    def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
        """
245
        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
246
247
248

        Args:
            num_inference_steps (`int`):
249
250
251
                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.
252
253
        """
        self.num_inference_steps = num_inference_steps
254
255
        # Clipping the minimum of all lambda(t) for numerical stability.
        # This is critical for cosine (squaredcos_cap_v2) noise schedule.
Patrick von Platen's avatar
Patrick von Platen committed
256
        clipped_idx = torch.searchsorted(torch.flip(self.lambda_t, [0]), self.config.lambda_min_clipped)
257
        timesteps = (
258
            np.linspace(0, self.config.num_train_timesteps - 1 - clipped_idx, num_inference_steps + 1)
259
260
261
262
            .round()[::-1][:-1]
            .copy()
            .astype(np.int64)
        )
263

264
265
        sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
        if self.config.use_karras_sigmas:
266
            log_sigmas = np.log(sigmas)
267
            sigmas = np.flip(sigmas).copy()
268
269
            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()
270
271
272
273
274
            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)
275

276
        self.sigmas = torch.from_numpy(sigmas).to(device=device)
277

278
        self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.int64)
279
280
        self.model_outputs = [None] * self.config.solver_order
        self.sample = None
Patrick von Platen's avatar
Patrick von Platen committed
281
282
283
284
285
286
287
288

        if not self.config.lower_order_final and num_inference_steps % self.config.solver_order != 0:
            logger.warn(
                "Changing scheduler {self.config} to have `lower_order_final` set to True to handle uneven amount of inference steps. Please make sure to always use an even number of `num_inference steps when using `lower_order_final=True`."
            )
            self.register_to_config(lower_order_final=True)

        self.order_list = self.get_order_list(num_inference_steps)
289

290
291
        # add an index counter for schedulers that allow duplicated timesteps
        self._step_index = None
292
        self.sigmas.to("cpu")  # to avoid too much CPU/GPU communication
293

294
295
    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler._threshold_sample
    def _threshold_sample(self, sample: torch.FloatTensor) -> torch.FloatTensor:
296
297
298
299
300
301
302
303
304
305
        """
        "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
306
        batch_size, channels, *remaining_dims = sample.shape
307
308
309
310
311

        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
312
        sample = sample.reshape(batch_size, channels * np.prod(remaining_dims))
313
314
315
316
317
318
319
320
321
322

        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"

323
        sample = sample.reshape(batch_size, channels, *remaining_dims)
324
325
326
        sample = sample.to(dtype)

        return sample
327

328
329
330
    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
    def _sigma_to_t(self, sigma, log_sigmas):
        # get log sigma
331
        log_sigma = np.log(np.maximum(sigma, 1e-10))
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351

        # 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

352
353
354
355
356
357
358
    # 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

359
360
361
362
    # 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)."""

Suraj Patil's avatar
Suraj Patil committed
363
364
365
366
367
368
369
370
371
372
373
374
375
376
        # 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()
377
378
379
380
381
382
383
384

        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

385
    def convert_model_output(
386
387
388
389
390
        self,
        model_output: torch.FloatTensor,
        *args,
        sample: torch.FloatTensor = None,
        **kwargs,
391
392
    ) -> torch.FloatTensor:
        """
393
394
395
396
397
        Convert the model output to the corresponding type the DPMSolver/DPMSolver++ algorithm needs. DPM-Solver is
        designed to discretize an integral of the noise prediction model, and DPM-Solver++ is designed to discretize an
        integral of the data prediction model.

        <Tip>
398

399
400
        The algorithm and model type are decoupled. You can use either DPMSolver or DPMSolver++ for both noise
        prediction and data prediction models.
401

402
        </Tip>
403
404

        Args:
405
406
            model_output (`torch.FloatTensor`):
                The direct output from the learned diffusion model.
407
            sample (`torch.FloatTensor`):
408
                A current instance of a sample created by the diffusion process.
409
410

        Returns:
411
412
            `torch.FloatTensor`:
                The converted model output.
413
        """
414
415
416
417
418
419
420
421
422
423
424
425
        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`",
            )
426
427
428
        # DPM-Solver++ needs to solve an integral of the data prediction model.
        if self.config.algorithm_type == "dpmsolver++":
            if self.config.prediction_type == "epsilon":
429
430
431
                # DPM-Solver and DPM-Solver++ only need the "mean" output.
                if self.config.variance_type in ["learned_range"]:
                    model_output = model_output[:, :3]
432
433
                sigma = self.sigmas[self.step_index]
                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
434
435
436
437
                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":
438
439
                sigma = self.sigmas[self.step_index]
                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
440
441
442
443
444
445
446
447
                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"
                    " `v_prediction` for the DPMSolverSinglestepScheduler."
                )

            if self.config.thresholding:
448
449
                x0_pred = self._threshold_sample(x0_pred)

450
451
452
453
            return x0_pred
        # DPM-Solver needs to solve an integral of the noise prediction model.
        elif self.config.algorithm_type == "dpmsolver":
            if self.config.prediction_type == "epsilon":
454
455
456
                # DPM-Solver and DPM-Solver++ only need the "mean" output.
                if self.config.variance_type in ["learned_range"]:
                    model_output = model_output[:, :3]
457
458
                return model_output
            elif self.config.prediction_type == "sample":
459
460
                sigma = self.sigmas[self.step_index]
                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
461
462
463
                epsilon = (sample - alpha_t * model_output) / sigma_t
                return epsilon
            elif self.config.prediction_type == "v_prediction":
464
465
                sigma = self.sigmas[self.step_index]
                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
466
467
468
469
470
471
472
473
474
475
476
                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"
                    " `v_prediction` for the DPMSolverSinglestepScheduler."
                )

    def dpm_solver_first_order_update(
        self,
        model_output: torch.FloatTensor,
477
478
479
        *args,
        sample: torch.FloatTensor = None,
        **kwargs,
480
481
    ) -> torch.FloatTensor:
        """
482
        One step for the first-order DPMSolver (equivalent to DDIM).
483
484

        Args:
485
486
487
488
489
490
            model_output (`torch.FloatTensor`):
                The direct output from the learned diffusion model.
            timestep (`int`):
                The current discrete timestep in the diffusion chain.
            prev_timestep (`int`):
                The previous discrete timestep in the diffusion chain.
491
            sample (`torch.FloatTensor`):
492
                A current instance of a sample created by the diffusion process.
493
494

        Returns:
495
496
            `torch.FloatTensor`:
                The sample tensor at the previous timestep.
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
        timestep = args[0] if len(args) > 0 else kwargs.pop("timestep", None)
        prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None)
        if sample is None:
            if len(args) > 2:
                sample = args[2]
            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`",
            )

        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`",
            )
        sigma_t, sigma_s = self.sigmas[self.step_index + 1], self.sigmas[self.step_index]
        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
        alpha_s, sigma_s = self._sigma_to_alpha_sigma_t(sigma_s)
        lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
        lambda_s = torch.log(alpha_s) - torch.log(sigma_s)
523
524
525
526
527
528
529
530
531
532
        h = lambda_t - lambda_s
        if self.config.algorithm_type == "dpmsolver++":
            x_t = (sigma_t / sigma_s) * sample - (alpha_t * (torch.exp(-h) - 1.0)) * model_output
        elif self.config.algorithm_type == "dpmsolver":
            x_t = (alpha_t / alpha_s) * sample - (sigma_t * (torch.exp(h) - 1.0)) * model_output
        return x_t

    def singlestep_dpm_solver_second_order_update(
        self,
        model_output_list: List[torch.FloatTensor],
533
534
535
        *args,
        sample: torch.FloatTensor = None,
        **kwargs,
536
537
    ) -> torch.FloatTensor:
        """
538
539
        One step for the second-order singlestep DPMSolver that computes the solution at time `prev_timestep` from the
        time `timestep_list[-2]`.
540
541
542

        Args:
            model_output_list (`List[torch.FloatTensor]`):
543
544
545
546
547
                The direct outputs from learned diffusion model at current and latter timesteps.
            timestep (`int`):
                The current and latter discrete timestep in the diffusion chain.
            prev_timestep (`int`):
                The previous discrete timestep in the diffusion chain.
548
            sample (`torch.FloatTensor`):
549
                A current instance of a sample created by the diffusion process.
550
551

        Returns:
552
553
            `torch.FloatTensor`:
                The sample tensor at the previous timestep.
554
        """
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
        timestep_list = args[0] if len(args) > 0 else kwargs.pop("timestep_list", None)
        prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None)
        if sample is None:
            if len(args) > 2:
                sample = args[2]
            else:
                raise ValueError(" missing `sample` as a required keyward argument")
        if timestep_list is not None:
            deprecate(
                "timestep_list",
                "1.0.0",
                "Passing `timestep_list` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
            )

        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`",
            )
        sigma_t, sigma_s0, sigma_s1 = (
            self.sigmas[self.step_index + 1],
            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)
        alpha_s1, sigma_s1 = self._sigma_to_alpha_sigma_t(sigma_s1)

        lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
        lambda_s0 = torch.log(alpha_s0) - torch.log(sigma_s0)
        lambda_s1 = torch.log(alpha_s1) - torch.log(sigma_s1)

589
        m0, m1 = model_output_list[-1], model_output_list[-2]
590

591
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
        h, h_0 = lambda_t - lambda_s1, lambda_s0 - lambda_s1
        r0 = h_0 / h
        D0, D1 = m1, (1.0 / r0) * (m0 - m1)
        if self.config.algorithm_type == "dpmsolver++":
            # See https://arxiv.org/abs/2211.01095 for detailed derivations
            if self.config.solver_type == "midpoint":
                x_t = (
                    (sigma_t / sigma_s1) * sample
                    - (alpha_t * (torch.exp(-h) - 1.0)) * D0
                    - 0.5 * (alpha_t * (torch.exp(-h) - 1.0)) * D1
                )
            elif self.config.solver_type == "heun":
                x_t = (
                    (sigma_t / sigma_s1) * sample
                    - (alpha_t * (torch.exp(-h) - 1.0)) * D0
                    + (alpha_t * ((torch.exp(-h) - 1.0) / h + 1.0)) * D1
                )
        elif self.config.algorithm_type == "dpmsolver":
            # See https://arxiv.org/abs/2206.00927 for detailed derivations
            if self.config.solver_type == "midpoint":
                x_t = (
                    (alpha_t / alpha_s1) * sample
                    - (sigma_t * (torch.exp(h) - 1.0)) * D0
                    - 0.5 * (sigma_t * (torch.exp(h) - 1.0)) * D1
                )
            elif self.config.solver_type == "heun":
                x_t = (
                    (alpha_t / alpha_s1) * sample
                    - (sigma_t * (torch.exp(h) - 1.0)) * D0
                    - (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1
                )
        return x_t

    def singlestep_dpm_solver_third_order_update(
        self,
        model_output_list: List[torch.FloatTensor],
627
628
629
        *args,
        sample: torch.FloatTensor = None,
        **kwargs,
630
631
    ) -> torch.FloatTensor:
        """
632
633
        One step for the third-order singlestep DPMSolver that computes the solution at time `prev_timestep` from the
        time `timestep_list[-3]`.
634
635
636

        Args:
            model_output_list (`List[torch.FloatTensor]`):
637
638
639
640
641
                The direct outputs from learned diffusion model at current and latter timesteps.
            timestep (`int`):
                The current and latter discrete timestep in the diffusion chain.
            prev_timestep (`int`):
                The previous discrete timestep in the diffusion chain.
642
            sample (`torch.FloatTensor`):
643
                A current instance of a sample created by diffusion process.
644
645

        Returns:
646
647
            `torch.FloatTensor`:
                The sample tensor at the previous timestep.
648
        """
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675

        timestep_list = args[0] if len(args) > 0 else kwargs.pop("timestep_list", None)
        prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None)
        if sample is None:
            if len(args) > 2:
                sample = args[2]
            else:
                raise ValueError(" missing`sample` as a required keyward argument")
        if timestep_list is not None:
            deprecate(
                "timestep_list",
                "1.0.0",
                "Passing `timestep_list` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
            )

        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`",
            )

        sigma_t, sigma_s0, sigma_s1, sigma_s2 = (
            self.sigmas[self.step_index + 1],
            self.sigmas[self.step_index],
            self.sigmas[self.step_index - 1],
            self.sigmas[self.step_index - 2],
676
        )
677
678
679
680
681
682
683
684
685
686
687
688
689

        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
        alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)
        alpha_s1, sigma_s1 = self._sigma_to_alpha_sigma_t(sigma_s1)
        alpha_s2, sigma_s2 = self._sigma_to_alpha_sigma_t(sigma_s2)

        lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
        lambda_s0 = torch.log(alpha_s0) - torch.log(sigma_s0)
        lambda_s1 = torch.log(alpha_s1) - torch.log(sigma_s1)
        lambda_s2 = torch.log(alpha_s2) - torch.log(sigma_s2)

        m0, m1, m2 = model_output_list[-1], model_output_list[-2], model_output_list[-3]

690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
        h, h_0, h_1 = lambda_t - lambda_s2, lambda_s0 - lambda_s2, lambda_s1 - lambda_s2
        r0, r1 = h_0 / h, h_1 / h
        D0 = m2
        D1_0, D1_1 = (1.0 / r1) * (m1 - m2), (1.0 / r0) * (m0 - m2)
        D1 = (r0 * D1_0 - r1 * D1_1) / (r0 - r1)
        D2 = 2.0 * (D1_1 - D1_0) / (r0 - r1)
        if self.config.algorithm_type == "dpmsolver++":
            # See https://arxiv.org/abs/2206.00927 for detailed derivations
            if self.config.solver_type == "midpoint":
                x_t = (
                    (sigma_t / sigma_s2) * sample
                    - (alpha_t * (torch.exp(-h) - 1.0)) * D0
                    + (alpha_t * ((torch.exp(-h) - 1.0) / h + 1.0)) * D1_1
                )
            elif self.config.solver_type == "heun":
                x_t = (
                    (sigma_t / sigma_s2) * sample
                    - (alpha_t * (torch.exp(-h) - 1.0)) * D0
                    + (alpha_t * ((torch.exp(-h) - 1.0) / h + 1.0)) * D1
                    - (alpha_t * ((torch.exp(-h) - 1.0 + h) / h**2 - 0.5)) * D2
                )
        elif self.config.algorithm_type == "dpmsolver":
            # See https://arxiv.org/abs/2206.00927 for detailed derivations
            if self.config.solver_type == "midpoint":
                x_t = (
                    (alpha_t / alpha_s2) * sample
                    - (sigma_t * (torch.exp(h) - 1.0)) * D0
                    - (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1_1
                )
            elif self.config.solver_type == "heun":
                x_t = (
                    (alpha_t / alpha_s2) * sample
                    - (sigma_t * (torch.exp(h) - 1.0)) * D0
                    - (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1
                    - (sigma_t * ((torch.exp(h) - 1.0 - h) / h**2 - 0.5)) * D2
                )
        return x_t

    def singlestep_dpm_solver_update(
        self,
        model_output_list: List[torch.FloatTensor],
731
732
733
734
        *args,
        sample: torch.FloatTensor = None,
        order: int = None,
        **kwargs,
735
736
    ) -> torch.FloatTensor:
        """
737
        One step for the singlestep DPMSolver.
738
739
740

        Args:
            model_output_list (`List[torch.FloatTensor]`):
741
742
743
744
745
                The direct outputs from learned diffusion model at current and latter timesteps.
            timestep (`int`):
                The current and latter discrete timestep in the diffusion chain.
            prev_timestep (`int`):
                The previous discrete timestep in the diffusion chain.
746
            sample (`torch.FloatTensor`):
747
                A current instance of a sample created by diffusion process.
748
            order (`int`):
749
                The solver order at this step.
750
751

        Returns:
752
753
            `torch.FloatTensor`:
                The sample tensor at the previous timestep.
754
        """
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
        timestep_list = args[0] if len(args) > 0 else kwargs.pop("timestep_list", None)
        prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None)
        if sample is None:
            if len(args) > 2:
                sample = args[2]
            else:
                raise ValueError(" missing`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 timestep_list is not None:
            deprecate(
                "timestep_list",
                "1.0.0",
                "Passing `timestep_list` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
            )

        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`",
            )

781
        if order == 1:
782
            return self.dpm_solver_first_order_update(model_output_list[-1], sample=sample)
783
        elif order == 2:
784
            return self.singlestep_dpm_solver_second_order_update(model_output_list, sample=sample)
785
        elif order == 3:
786
            return self.singlestep_dpm_solver_third_order_update(model_output_list, sample=sample)
787
788
789
        else:
            raise ValueError(f"Order must be 1, 2, 3, got {order}")

790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
    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

809
810
811
812
813
814
815
816
    def step(
        self,
        model_output: torch.FloatTensor,
        timestep: int,
        sample: torch.FloatTensor,
        return_dict: bool = True,
    ) -> Union[SchedulerOutput, Tuple]:
        """
817
818
        Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
        the singlestep DPMSolver.
819
820

        Args:
821
822
823
824
            model_output (`torch.FloatTensor`):
                The direct output from learned diffusion model.
            timestep (`int`):
                The current discrete timestep in the diffusion chain.
825
            sample (`torch.FloatTensor`):
826
827
828
                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`.
829
830

        Returns:
831
832
833
            [`~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.
834
835
836
837
838
839
840

        """
        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"
            )

841
842
        if self.step_index is None:
            self._init_step_index(timestep)
843

844
        model_output = self.convert_model_output(model_output, sample=sample)
845
846
847
848
        for i in range(self.config.solver_order - 1):
            self.model_outputs[i] = self.model_outputs[i + 1]
        self.model_outputs[-1] = model_output

849
        order = self.order_list[self.step_index]
Patrick von Platen's avatar
Patrick von Platen committed
850
851
852
853
854
855

        #  For img2img denoising might start with order>1 which is not possible
        #  In this case make sure that the first two steps are both order=1
        while self.model_outputs[-order] is None:
            order -= 1

856
857
858
859
        # For single-step solvers, we use the initial value at each time with order = 1.
        if order == 1:
            self.sample = sample

860
861
862
863
        prev_sample = self.singlestep_dpm_solver_update(self.model_outputs, sample=self.sample, order=order)

        # upon completion increase step index by one
        self._step_index += 1
864
865
866
867
868
869
870
871
872
873
874
875

        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:
876
877
            sample (`torch.FloatTensor`):
                The input sample.
878
879

        Returns:
880
881
            `torch.FloatTensor`:
                A scaled input sample.
882
883
884
        """
        return sample

885
    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.add_noise
886
887
888
889
    def add_noise(
        self,
        original_samples: torch.FloatTensor,
        noise: torch.FloatTensor,
890
        timesteps: torch.IntTensor,
891
    ) -> torch.FloatTensor:
892
893
894
895
896
897
898
899
900
        # 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)
901

902
903
904
905
906
907
908
909
910
911
        step_indices = []
        for timestep in timesteps:
            index_candidates = (schedule_timesteps == timestep).nonzero()
            if len(index_candidates) == 0:
                step_index = len(schedule_timesteps) - 1
            elif len(index_candidates) > 1:
                step_index = index_candidates[1].item()
            else:
                step_index = index_candidates[0].item()
            step_indices.append(step_index)
912

913
914
915
        sigma = sigmas[step_indices].flatten()
        while len(sigma.shape) < len(original_samples.shape):
            sigma = sigma.unsqueeze(-1)
916

917
918
        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
        noisy_samples = alpha_t * original_samples + sigma_t * noise
919
920
921
922
        return noisy_samples

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