scheduling_dpmsolver_multistep.py 46.5 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
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
Dhruv Nair's avatar
Dhruv Nair committed
25
from ..utils.torch_utils import randn_tensor
Kashif Rasul's avatar
Kashif Rasul committed
26
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
27
28


29
# Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar
YiYi Xu's avatar
YiYi Xu committed
30
31
32
33
34
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.
YiYi Xu's avatar
YiYi Xu committed
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
    """
YiYi Xu's avatar
YiYi Xu committed
53
    if alpha_transform_type == "cosine":
54

YiYi Xu's avatar
YiYi Xu committed
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
YiYi Xu's avatar
YiYi Xu committed
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
81
82
83
84
85
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
# 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:
        betas (`torch.FloatTensor`):
            the betas that the scheduler is being initialized with.

    Returns:
        `torch.FloatTensor`: rescaled betas with zero terminal SNR
    """
    # 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 DPMSolverMultistepScheduler(SchedulerMixin, ConfigMixin):
    """
113
    `DPMSolverMultistepScheduler` is a fast dedicated high-order solver for diffusion ODEs.
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
130
131
        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
132
            sampling, and `solver_order=3` for unconditional sampling.
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
        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.
157
158
159
160
        euler_at_final (`bool`, defaults to `False`):
            Whether to use Euler's method in the final step. It is a trade-off between numerical stability and detail
            richness. This can stabilize the sampling of the SDE variant of DPMSolver for small number of inference
            steps, but sometimes may result in blurring.
161
        use_karras_sigmas (`bool`, *optional*, defaults to `False`):
162
163
            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}.
164
165
166
167
        use_lu_lambdas (`bool`, *optional*, defaults to `False`):
            Whether to use the uniform-logSNR for step sizes proposed by Lu's DPM-Solver in the noise schedule during
            the sampling process. If `True`, the sigmas and time steps are determined according to a sequence of
            `lambda(t)`.
168
169
170
        final_sigmas_type (`str`, defaults to `"zero"`):
            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.
171
172
173
        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.
174
        variance_type (`str`, *optional*):
175
176
177
178
179
180
            Set to "learned" or "learned_range" for diffusion models that predict variance. If set, the model's output
            contains the predicted Gaussian variance.
        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):
181
            An offset added to the inference steps, as required by some model families.
182
183
184
185
        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).
186
187
    """

Kashif Rasul's avatar
Kashif Rasul committed
188
    _compatibles = [e.name for e in KarrasDiffusionSchedulers]
189
    order = 1
190
191
192
193
194
195
196
197

    @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",
198
        trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
199
        solver_order: int = 2,
200
        prediction_type: str = "epsilon",
201
202
203
204
205
206
        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,
207
        euler_at_final: bool = False,
208
        use_karras_sigmas: Optional[bool] = False,
209
        use_lu_lambdas: Optional[bool] = False,
210
        final_sigmas_type: Optional[str] = "zero",  # "zero", "sigma_min"
211
212
        lambda_min_clipped: float = -float("inf"),
        variance_type: Optional[str] = None,
213
214
        timestep_spacing: str = "linspace",
        steps_offset: int = 0,
215
        rescale_betas_zero_snr: bool = False,
216
    ):
217
218
219
220
        if algorithm_type in ["dpmsolver", "sde-dpmsolver"]:
            deprecation_message = f"algorithm_type {algorithm_type} is deprecated and will be removed in a future version. Choose from `dpmsolver++` or `sde-dpmsolver++` instead"
            deprecate("algorithm_types dpmsolver and sde-dpmsolver", "1.0.0", deprecation_message)

221
        if trained_betas is not None:
222
            self.betas = torch.tensor(trained_betas, dtype=torch.float32)
223
224
225
226
        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.
227
            self.betas = torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2
228
229
230
231
232
233
        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__}")

234
235
236
        if rescale_betas_zero_snr:
            self.betas = rescale_zero_terminal_snr(self.betas)

237
238
        self.alphas = 1.0 - self.betas
        self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
239
240
241
242
243
244

        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

245
246
247
248
        # 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)
249
        self.sigmas = ((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5
250
251
252
253
254

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

        # settings for DPM-Solver
255
        if algorithm_type not in ["dpmsolver", "dpmsolver++", "sde-dpmsolver", "sde-dpmsolver++"]:
256
            if algorithm_type == "deis":
257
                self.register_to_config(algorithm_type="dpmsolver++")
258
259
            else:
                raise NotImplementedError(f"{algorithm_type} does is not implemented for {self.__class__}")
260

261
        if solver_type not in ["midpoint", "heun"]:
262
            if solver_type in ["logrho", "bh1", "bh2"]:
263
                self.register_to_config(solver_type="midpoint")
264
265
            else:
                raise NotImplementedError(f"{solver_type} does is not implemented for {self.__class__}")
266

267
268
269
270
271
        if algorithm_type not in ["dpmsolver++", "sde-dpmsolver++"] and final_sigmas_type == "zero":
            raise ValueError(
                f"`final_sigmas_type` {final_sigmas_type} is not supported for `algorithm_type` {algorithm_type}. Please choose `sigma_min` instead."
            )

272
273
274
275
276
277
        # 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.lower_order_nums = 0
278
        self._step_index = None
279
        self._begin_index = None
280
        self.sigmas = self.sigmas.to("cpu")  # to avoid too much CPU/GPU communication
281
282
283
284

    @property
    def step_index(self):
        """
M. Tolga Cangöz's avatar
M. Tolga Cangöz committed
285
        The index counter for current timestep. It will increase 1 after each scheduler step.
286
287
        """
        return self._step_index
288

289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
    @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

    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

306
    def set_timesteps(self, num_inference_steps: int = None, device: Union[str, torch.device] = None):
307
        """
308
        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
309
310
311

        Args:
            num_inference_steps (`int`):
312
313
314
                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.
315
        """
316
317
        # Clipping the minimum of all lambda(t) for numerical stability.
        # This is critical for cosine (squaredcos_cap_v2) noise schedule.
318
        clipped_idx = torch.searchsorted(torch.flip(self.lambda_t, [0]), self.config.lambda_min_clipped)
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
        last_timestep = ((self.config.num_train_timesteps - clipped_idx).numpy()).item()

        # "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, last_timestep - 1, num_inference_steps + 1).round()[::-1][:-1].copy().astype(np.int64)
            )
        elif self.config.timestep_spacing == "leading":
            step_ratio = last_timestep // (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(last_timestep, 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'."
            )
342

343
        sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
344
345
        log_sigmas = np.log(sigmas)

346
        if self.config.use_karras_sigmas:
347
            sigmas = np.flip(sigmas).copy()
348
349
            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()
350
351
352
353
354
        elif self.config.use_lu_lambdas:
            lambdas = np.flip(log_sigmas.copy())
            lambdas = self._convert_to_lu(in_lambdas=lambdas, num_inference_steps=num_inference_steps)
            sigmas = np.exp(lambdas)
            timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]).round()
355
356
        else:
            sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
357
358

        if self.config.final_sigmas_type == "sigma_min":
359
            sigma_last = ((1 - self.alphas_cumprod[0]) / self.alphas_cumprod[0]) ** 0.5
360
361
362
363
364
365
366
367
        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)
368

369
370
        self.sigmas = torch.from_numpy(sigmas)
        self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.int64)
371
372
373

        self.num_inference_steps = len(timesteps)

374
375
376
377
378
        self.model_outputs = [
            None,
        ] * self.config.solver_order
        self.lower_order_nums = 0

379
380
        # add an index counter for schedulers that allow duplicated timesteps
        self._step_index = None
381
        self._begin_index = None
382
        self.sigmas = self.sigmas.to("cpu")  # to avoid too much CPU/GPU communication
383

384
385
    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler._threshold_sample
    def _threshold_sample(self, sample: torch.FloatTensor) -> torch.FloatTensor:
386
387
388
389
390
391
392
393
394
395
        """
        "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
396
        batch_size, channels, *remaining_dims = sample.shape
397
398
399
400
401

        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
402
        sample = sample.reshape(batch_size, channels * np.prod(remaining_dims))
403
404
405
406
407
408
409
410
411
412

        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"

413
        sample = sample.reshape(batch_size, channels, *remaining_dims)
414
415
416
        sample = sample.to(dtype)

        return sample
417

418
419
420
    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
    def _sigma_to_t(self, sigma, log_sigmas):
        # get log sigma
421
        log_sigma = np.log(np.maximum(sigma, 1e-10))
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441

        # 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

442
443
444
445
446
447
    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

448
449
450
451
    # 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
452
453
454
455
456
457
458
459
460
461
462
463
464
465
        # 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()
466
467
468
469
470
471
472
473

        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

474
475
476
477
478
479
480
481
482
483
484
485
486
    def _convert_to_lu(self, in_lambdas: torch.FloatTensor, num_inference_steps) -> torch.FloatTensor:
        """Constructs the noise schedule of Lu et al. (2022)."""

        lambda_min: float = in_lambdas[-1].item()
        lambda_max: float = in_lambdas[0].item()

        rho = 1.0  # 1.0 is the value used in the paper
        ramp = np.linspace(0, 1, num_inference_steps)
        min_inv_rho = lambda_min ** (1 / rho)
        max_inv_rho = lambda_max ** (1 / rho)
        lambdas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
        return lambdas

487
    def convert_model_output(
488
489
490
491
492
        self,
        model_output: torch.FloatTensor,
        *args,
        sample: torch.FloatTensor = None,
        **kwargs,
493
494
    ) -> torch.FloatTensor:
        """
495
496
497
        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.
498

499
        <Tip>
500

501
502
503
504
        The algorithm and model type are decoupled. You can use either DPMSolver or DPMSolver++ for both noise
        prediction and data prediction models.

        </Tip>
505
506

        Args:
507
508
            model_output (`torch.FloatTensor`):
                The direct output from the learned diffusion model.
509
            sample (`torch.FloatTensor`):
510
                A current instance of a sample created by the diffusion process.
511
512

        Returns:
513
514
            `torch.FloatTensor`:
                The converted model output.
515
        """
516
517
518
519
520
521
522
523
524
525
526
527
        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`",
            )
528

529
        # DPM-Solver++ needs to solve an integral of the data prediction model.
530
        if self.config.algorithm_type in ["dpmsolver++", "sde-dpmsolver++"]:
531
            if self.config.prediction_type == "epsilon":
532
                # DPM-Solver and DPM-Solver++ only need the "mean" output.
533
                if self.config.variance_type in ["learned", "learned_range"]:
534
                    model_output = model_output[:, :3]
535
536
                sigma = self.sigmas[self.step_index]
                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
537
                x0_pred = (sample - sigma_t * model_output) / alpha_t
538
            elif self.config.prediction_type == "sample":
539
                x0_pred = model_output
540
            elif self.config.prediction_type == "v_prediction":
541
542
                sigma = self.sigmas[self.step_index]
                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
543
                x0_pred = alpha_t * sample - sigma_t * model_output
544
545
            else:
                raise ValueError(
546
547
                    f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
                    " `v_prediction` for the DPMSolverMultistepScheduler."
548
549
                )

550
            if self.config.thresholding:
551
552
                x0_pred = self._threshold_sample(x0_pred)

553
            return x0_pred
554

555
        # DPM-Solver needs to solve an integral of the noise prediction model.
556
        elif self.config.algorithm_type in ["dpmsolver", "sde-dpmsolver"]:
557
            if self.config.prediction_type == "epsilon":
558
                # DPM-Solver and DPM-Solver++ only need the "mean" output.
559
560
561
562
                if self.config.variance_type in ["learned", "learned_range"]:
                    epsilon = model_output[:, :3]
                else:
                    epsilon = model_output
563
            elif self.config.prediction_type == "sample":
564
565
                sigma = self.sigmas[self.step_index]
                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
566
                epsilon = (sample - alpha_t * model_output) / sigma_t
567
            elif self.config.prediction_type == "v_prediction":
568
569
                sigma = self.sigmas[self.step_index]
                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
570
                epsilon = alpha_t * model_output + sigma_t * sample
571
572
            else:
                raise ValueError(
573
574
                    f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
                    " `v_prediction` for the DPMSolverMultistepScheduler."
575
                )
576

577
            if self.config.thresholding:
578
579
                sigma = self.sigmas[self.step_index]
                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
580
581
582
583
584
585
                x0_pred = (sample - sigma_t * epsilon) / alpha_t
                x0_pred = self._threshold_sample(x0_pred)
                epsilon = (sample - alpha_t * x0_pred) / sigma_t

            return epsilon

586
587
588
    def dpm_solver_first_order_update(
        self,
        model_output: torch.FloatTensor,
589
590
        *args,
        sample: torch.FloatTensor = None,
591
        noise: Optional[torch.FloatTensor] = None,
592
        **kwargs,
593
594
    ) -> torch.FloatTensor:
        """
595
        One step for the first-order DPMSolver (equivalent to DDIM).
596
597

        Args:
598
599
            model_output (`torch.FloatTensor`):
                The direct output from the learned diffusion model.
600
            sample (`torch.FloatTensor`):
601
                A current instance of a sample created by the diffusion process.
602
603

        Returns:
604
605
            `torch.FloatTensor`:
                The sample tensor at the previous timestep.
606
        """
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
        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)

634
635
636
637
638
        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
639
640
641
642
643
644
645
646
647
648
649
650
651
652
        elif self.config.algorithm_type == "sde-dpmsolver++":
            assert noise is not None
            x_t = (
                (sigma_t / sigma_s * torch.exp(-h)) * sample
                + (alpha_t * (1 - torch.exp(-2.0 * h))) * model_output
                + sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise
            )
        elif self.config.algorithm_type == "sde-dpmsolver":
            assert noise is not None
            x_t = (
                (alpha_t / alpha_s) * sample
                - 2.0 * (sigma_t * (torch.exp(h) - 1.0)) * model_output
                + sigma_t * torch.sqrt(torch.exp(2 * h) - 1.0) * noise
            )
653
654
655
656
657
        return x_t

    def multistep_dpm_solver_second_order_update(
        self,
        model_output_list: List[torch.FloatTensor],
658
659
        *args,
        sample: torch.FloatTensor = None,
660
        noise: Optional[torch.FloatTensor] = None,
661
        **kwargs,
662
663
    ) -> torch.FloatTensor:
        """
664
        One step for the second-order multistep DPMSolver.
665
666
667

        Args:
            model_output_list (`List[torch.FloatTensor]`):
668
                The direct outputs from learned diffusion model at current and latter timesteps.
669
            sample (`torch.FloatTensor`):
670
                A current instance of a sample created by the diffusion process.
671
672

        Returns:
673
674
            `torch.FloatTensor`:
                The sample tensor at the previous timestep.
675
        """
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
        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)

711
        m0, m1 = model_output_list[-1], model_output_list[-2]
712

713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
        h, h_0 = lambda_t - lambda_s0, lambda_s0 - lambda_s1
        r0 = h_0 / h
        D0, D1 = m0, (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_s0) * 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_s0) * 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_s0) * 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_s0) * sample
                    - (sigma_t * (torch.exp(h) - 1.0)) * D0
                    - (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1
                )
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
        elif self.config.algorithm_type == "sde-dpmsolver++":
            assert noise is not None
            if self.config.solver_type == "midpoint":
                x_t = (
                    (sigma_t / sigma_s0 * torch.exp(-h)) * sample
                    + (alpha_t * (1 - torch.exp(-2.0 * h))) * D0
                    + 0.5 * (alpha_t * (1 - torch.exp(-2.0 * h))) * D1
                    + sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise
                )
            elif self.config.solver_type == "heun":
                x_t = (
                    (sigma_t / sigma_s0 * torch.exp(-h)) * sample
                    + (alpha_t * (1 - torch.exp(-2.0 * h))) * D0
                    + (alpha_t * ((1.0 - torch.exp(-2.0 * h)) / (-2.0 * h) + 1.0)) * D1
                    + sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise
                )
        elif self.config.algorithm_type == "sde-dpmsolver":
            assert noise is not None
            if self.config.solver_type == "midpoint":
                x_t = (
                    (alpha_t / alpha_s0) * sample
                    - 2.0 * (sigma_t * (torch.exp(h) - 1.0)) * D0
                    - (sigma_t * (torch.exp(h) - 1.0)) * D1
                    + sigma_t * torch.sqrt(torch.exp(2 * h) - 1.0) * noise
                )
            elif self.config.solver_type == "heun":
                x_t = (
                    (alpha_t / alpha_s0) * sample
                    - 2.0 * (sigma_t * (torch.exp(h) - 1.0)) * D0
                    - 2.0 * (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1
                    + sigma_t * torch.sqrt(torch.exp(2 * h) - 1.0) * noise
                )
776
777
778
779
780
        return x_t

    def multistep_dpm_solver_third_order_update(
        self,
        model_output_list: List[torch.FloatTensor],
781
782
783
        *args,
        sample: torch.FloatTensor = None,
        **kwargs,
784
785
    ) -> torch.FloatTensor:
        """
786
        One step for the third-order multistep DPMSolver.
787
788
789

        Args:
            model_output_list (`List[torch.FloatTensor]`):
790
                The direct outputs from learned diffusion model at current and latter timesteps.
791
            sample (`torch.FloatTensor`):
792
                A current instance of a sample created by diffusion process.
793
794

        Returns:
795
796
            `torch.FloatTensor`:
                The sample tensor at the previous timestep.
797
        """
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824

        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],
825
        )
826
827
828
829
830
831
832
833
834
835
836
837
838

        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]

839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
        h, h_0, h_1 = lambda_t - lambda_s0, lambda_s0 - lambda_s1, lambda_s1 - lambda_s2
        r0, r1 = h_0 / h, h_1 / h
        D0 = m0
        D1_0, D1_1 = (1.0 / r0) * (m0 - m1), (1.0 / r1) * (m1 - m2)
        D1 = D1_0 + (r0 / (r0 + r1)) * (D1_0 - D1_1)
        D2 = (1.0 / (r0 + r1)) * (D1_0 - D1_1)
        if self.config.algorithm_type == "dpmsolver++":
            # See https://arxiv.org/abs/2206.00927 for detailed derivations
            x_t = (
                (sigma_t / sigma_s0) * 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
            x_t = (
                (alpha_t / alpha_s0) * 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

863
864
865
    def index_for_timestep(self, timestep, schedule_timesteps=None):
        if schedule_timesteps is None:
            schedule_timesteps = self.timesteps
866

867
        index_candidates = (schedule_timesteps == timestep).nonzero()
868
869
870
871
872
873
874
875
876
877
878
879

        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()

880
881
882
883
884
885
886
887
888
889
890
891
892
        return 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
893

894
895
896
897
898
    def step(
        self,
        model_output: torch.FloatTensor,
        timestep: int,
        sample: torch.FloatTensor,
899
        generator=None,
900
        variance_noise: Optional[torch.FloatTensor] = None,
901
902
903
        return_dict: bool = True,
    ) -> Union[SchedulerOutput, Tuple]:
        """
904
905
        Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
        the multistep DPMSolver.
906
907

        Args:
908
909
910
911
            model_output (`torch.FloatTensor`):
                The direct output from learned diffusion model.
            timestep (`int`):
                The current discrete timestep in the diffusion chain.
912
            sample (`torch.FloatTensor`):
913
914
915
                A current instance of a sample created by the diffusion process.
            generator (`torch.Generator`, *optional*):
                A random number generator.
916
917
918
            variance_noise (`torch.FloatTensor`):
                Alternative to generating noise with `generator` by directly providing the noise for the variance
                itself. Useful for methods such as [`LEdits++`].
919
920
            return_dict (`bool`):
                Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`.
921
922

        Returns:
923
924
925
            [`~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.
926
927
928
929
930
931
932

        """
        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"
            )

933
934
935
        if self.step_index is None:
            self._init_step_index(timestep)

936
937
        # Improve numerical stability for small number of steps
        lower_order_final = (self.step_index == len(self.timesteps) - 1) and (
938
939
940
            self.config.euler_at_final
            or (self.config.lower_order_final and len(self.timesteps) < 15)
            or self.config.final_sigmas_type == "zero"
941
942
        )
        lower_order_second = (
943
            (self.step_index == len(self.timesteps) - 2) and self.config.lower_order_final and len(self.timesteps) < 15
944
945
        )

946
        model_output = self.convert_model_output(model_output, sample=sample)
947
948
949
950
        for i in range(self.config.solver_order - 1):
            self.model_outputs[i] = self.model_outputs[i + 1]
        self.model_outputs[-1] = model_output

951
952
        # Upcast to avoid precision issues when computing prev_sample
        sample = sample.to(torch.float32)
953
        if self.config.algorithm_type in ["sde-dpmsolver", "sde-dpmsolver++"] and variance_noise is None:
954
            noise = randn_tensor(
955
                model_output.shape, generator=generator, device=model_output.device, dtype=torch.float32
956
            )
957
958
        elif self.config.algorithm_type in ["sde-dpmsolver", "sde-dpmsolver++"]:
            noise = variance_noise.to(device=model_output.device, dtype=torch.float32)
959
960
961
        else:
            noise = None

962
        if self.config.solver_order == 1 or self.lower_order_nums < 1 or lower_order_final:
963
            prev_sample = self.dpm_solver_first_order_update(model_output, sample=sample, noise=noise)
964
        elif self.config.solver_order == 2 or self.lower_order_nums < 2 or lower_order_second:
965
            prev_sample = self.multistep_dpm_solver_second_order_update(self.model_outputs, sample=sample, noise=noise)
966
        else:
967
            prev_sample = self.multistep_dpm_solver_third_order_update(self.model_outputs, sample=sample)
968
969
970
971

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

972
973
974
        # Cast sample back to expected dtype
        prev_sample = prev_sample.to(model_output.dtype)

975
976
977
        # upon completion increase step index by one
        self._step_index += 1

978
979
980
981
982
983
984
985
986
987
988
        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:
989
990
            sample (`torch.FloatTensor`):
                The input sample.
991
992

        Returns:
993
994
            `torch.FloatTensor`:
                A scaled input sample.
995
996
997
998
999
1000
1001
        """
        return sample

    def add_noise(
        self,
        original_samples: torch.FloatTensor,
        noise: torch.FloatTensor,
1002
        timesteps: torch.IntTensor,
1003
    ) -> torch.FloatTensor:
1004
1005
1006
1007
1008
1009
1010
1011
1012
        # 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)
1013

1014
1015
1016
1017
1018
        # begin_index is None when the scheduler is used for training
        if self.begin_index is None:
            step_indices = [self.index_for_timestep(t, schedule_timesteps) for t in timesteps]
        else:
            step_indices = [self.begin_index] * timesteps.shape[0]
1019

1020
1021
1022
        sigma = sigmas[step_indices].flatten()
        while len(sigma.shape) < len(original_samples.shape):
            sigma = sigma.unsqueeze(-1)
1023

1024
1025
        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
        noisy_samples = alpha_t * original_samples + sigma_t * noise
1026
1027
1028
1029
        return noisy_samples

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