scheduling_dpmsolver_multistep_inverse.py 41.6 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
# Copyright 2023 TSAIL Team and The HuggingFace Team. All rights reserved.
#
# 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
26
27
28
29
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput


# 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
64
        def alpha_bar_fn(t):
            return math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2

    elif alpha_transform_type == "exp":

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

    else:
        raise ValueError(f"Unsupported alpha_tranform_type: {alpha_transform_type}")
65
66
67
68
69

    betas = []
    for i in range(num_diffusion_timesteps):
        t1 = i / num_diffusion_timesteps
        t2 = (i + 1) / num_diffusion_timesteps
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
74
75
    return torch.tensor(betas, dtype=torch.float32)


class DPMSolverMultistepInverseScheduler(SchedulerMixin, ConfigMixin):
    """
76
    `DPMSolverMultistepInverseScheduler` is the reverse scheduler of [`DPMSolverMultistepScheduler`].
77

78
79
    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
    methods the library implements for all schedulers such as loading and saving.
80
81

    Args:
82
83
84
85
86
87
88
89
        num_train_timesteps (`int`, defaults to 1000):
            The number of diffusion steps to train the model.
        beta_start (`float`, defaults to 0.0001):
            The starting `beta` value of inference.
        beta_end (`float`, defaults to 0.02):
            The final `beta` value.
        beta_schedule (`str`, defaults to `"linear"`):
            The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
90
            `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
91
92
93
94
        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
95
            sampling, and `solver_order=3` for unconditional sampling.
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
        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.
120
121
122
123
        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.
124
        use_karras_sigmas (`bool`, *optional*, defaults to `False`):
125
126
127
128
129
            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.
130
        variance_type (`str`, *optional*):
131
132
133
134
135
136
137
138
139
            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):
            An offset added to the inference steps. You can use a combination of `offset=1` and
            `set_alpha_to_one=False` to make the last step use step 0 for the previous alpha product like in Stable
            Diffusion.
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
    """

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

    @register_to_config
    def __init__(
        self,
        num_train_timesteps: int = 1000,
        beta_start: float = 0.0001,
        beta_end: float = 0.02,
        beta_schedule: str = "linear",
        trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
        solver_order: int = 2,
        prediction_type: str = "epsilon",
        thresholding: bool = False,
        dynamic_thresholding_ratio: float = 0.995,
        sample_max_value: float = 1.0,
        algorithm_type: str = "dpmsolver++",
        solver_type: str = "midpoint",
        lower_order_final: bool = True,
161
        euler_at_final: bool = False,
162
163
164
        use_karras_sigmas: Optional[bool] = False,
        lambda_min_clipped: float = -float("inf"),
        variance_type: Optional[str] = None,
165
166
        timestep_spacing: str = "linspace",
        steps_offset: int = 0,
167
168
169
170
171
172
173
    ):
        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.
174
            self.betas = torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
        elif beta_schedule == "squaredcos_cap_v2":
            # Glide cosine schedule
            self.betas = betas_for_alpha_bar(num_train_timesteps)
        else:
            raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}")

        self.alphas = 1.0 - self.betas
        self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
        # Currently we only support VP-type noise schedule
        self.alpha_t = torch.sqrt(self.alphas_cumprod)
        self.sigma_t = torch.sqrt(1 - self.alphas_cumprod)
        self.lambda_t = torch.log(self.alpha_t) - torch.log(self.sigma_t)

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

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

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

        # setable values
        self.num_inference_steps = None
        timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=np.float32).copy()
        self.timesteps = torch.from_numpy(timesteps)
        self.model_outputs = [None] * solver_order
        self.lower_order_nums = 0
210
        self._step_index = None
211
212
        self.use_karras_sigmas = use_karras_sigmas

213
214
215
216
217
218
219
    @property
    def step_index(self):
        """
        The index counter for current timestep. It will increae 1 after each scheduler step.
        """
        return self._step_index

220
221
    def set_timesteps(self, num_inference_steps: int = None, device: Union[str, torch.device] = None):
        """
222
        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
223
224
225

        Args:
            num_inference_steps (`int`):
226
227
228
                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.
229
230
231
        """
        # Clipping the minimum of all lambda(t) for numerical stability.
        # This is critical for cosine (squaredcos_cap_v2) noise schedule.
232
        clipped_idx = torch.searchsorted(torch.flip(self.lambda_t, [0]), self.lambda_min_clipped).item()
233
234
        self.noisiest_timestep = self.config.num_train_timesteps - 1 - clipped_idx

235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
        # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
        if self.config.timestep_spacing == "linspace":
            timesteps = (
                np.linspace(0, self.noisiest_timestep, num_inference_steps + 1).round()[:-1].copy().astype(np.int64)
            )
        elif self.config.timestep_spacing == "leading":
            step_ratio = (self.noisiest_timestep + 1) // (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].copy().astype(np.int64)
            timesteps += self.config.steps_offset
        elif self.config.timestep_spacing == "trailing":
            step_ratio = self.config.num_train_timesteps / num_inference_steps
            # creates integer timesteps by multiplying by ratio
            # casting to int to avoid issues when num_inference_step is power of 3
            timesteps = np.arange(self.noisiest_timestep + 1, 0, -step_ratio).round()[::-1].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'."
            )

        sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
259
260
        log_sigmas = np.log(sigmas)

261
        if self.config.use_karras_sigmas:
262
263
264
            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()
            timesteps = timesteps.copy().astype(np.int64)
265
266
267
268
269
270
271
            sigmas = np.concatenate([sigmas, sigmas[-1:]]).astype(np.float32)
        else:
            sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
            sigma_max = (
                (1 - self.alphas_cumprod[self.noisiest_timestep]) / self.alphas_cumprod[self.noisiest_timestep]
            ) ** 0.5
            sigmas = np.concatenate([sigmas, [sigma_max]]).astype(np.float32)
272

273
274
        self.sigmas = torch.from_numpy(sigmas)

275
276
277
278
279
        # when num_inference_steps == num_train_timesteps, we can end up with
        # duplicates in timesteps.
        _, unique_indices = np.unique(timesteps, return_index=True)
        timesteps = timesteps[np.sort(unique_indices)]

280
        self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.int64)
281
282
283
284
285
286
287
288

        self.num_inference_steps = len(timesteps)

        self.model_outputs = [
            None,
        ] * self.config.solver_order
        self.lower_order_nums = 0

289
290
291
        # add an index counter for schedulers that allow duplicated timesteps
        self._step_index = None

292
293
294
295
296
297
298
299
300
301
302
303
    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler._threshold_sample
    def _threshold_sample(self, sample: torch.FloatTensor) -> torch.FloatTensor:
        """
        "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
304
        batch_size, channels, *remaining_dims = sample.shape
305
306
307
308
309

        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
310
        sample = sample.reshape(batch_size, channels * np.prod(remaining_dims))
311
312
313
314
315
316
317
318
319
320

        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"

321
        sample = sample.reshape(batch_size, channels, *remaining_dims)
322
323
324
325
326
327
328
        sample = sample.to(dtype)

        return sample

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

        # 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

350
351
352
353
354
355
356
    # 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

357
358
359
360
    # 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
361
362
363
364
365
366
367
368
369
370
371
372
373
374
        # 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()
375
376
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

    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.convert_model_output
    def convert_model_output(
385
386
387
388
389
        self,
        model_output: torch.FloatTensor,
        *args,
        sample: torch.FloatTensor = None,
        **kwargs,
390
391
    ) -> torch.FloatTensor:
        """
392
393
394
395
396
        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>
397

398
399
        The algorithm and model type are decoupled. You can use either DPMSolver or DPMSolver++ for both noise
        prediction and data prediction models.
400

401
        </Tip>
402
403

        Args:
404
405
            model_output (`torch.FloatTensor`):
                The direct output from the learned diffusion model.
406
            sample (`torch.FloatTensor`):
407
                A current instance of a sample created by the diffusion process.
408
409

        Returns:
410
411
            `torch.FloatTensor`:
                The converted model output.
412
        """
413
414
415
416
417
418
419
420
421
422
423
424
        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`",
            )
425
426
427
428
429
430
431

        # DPM-Solver++ needs to solve an integral of the data prediction model.
        if self.config.algorithm_type in ["dpmsolver++", "sde-dpmsolver++"]:
            if self.config.prediction_type == "epsilon":
                # DPM-Solver and DPM-Solver++ only need the "mean" output.
                if self.config.variance_type in ["learned", "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
448
449
450
451
452
453
454
455
456
457
458
459
460
                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 DPMSolverMultistepScheduler."
                )

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

            return x0_pred

        # DPM-Solver needs to solve an integral of the noise prediction model.
        elif self.config.algorithm_type in ["dpmsolver", "sde-dpmsolver"]:
            if self.config.prediction_type == "epsilon":
                # DPM-Solver and DPM-Solver++ only need the "mean" output.
                if self.config.variance_type in ["learned", "learned_range"]:
                    epsilon = model_output[:, :3]
                else:
                    epsilon = model_output
            elif self.config.prediction_type == "sample":
461
462
                sigma = self.sigmas[self.step_index]
                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
463
464
                epsilon = (sample - alpha_t * model_output) / sigma_t
            elif self.config.prediction_type == "v_prediction":
465
466
                sigma = self.sigmas[self.step_index]
                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
467
468
469
470
471
472
473
474
                epsilon = alpha_t * model_output + sigma_t * sample
            else:
                raise ValueError(
                    f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
                    " `v_prediction` for the DPMSolverMultistepScheduler."
                )

            if self.config.thresholding:
475
476
                sigma = self.sigmas[self.step_index]
                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
477
478
479
480
481
482
                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

483
    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.dpm_solver_first_order_update
484
485
486
    def dpm_solver_first_order_update(
        self,
        model_output: torch.FloatTensor,
487
488
        *args,
        sample: torch.FloatTensor = None,
489
        noise: Optional[torch.FloatTensor] = None,
490
        **kwargs,
491
492
    ) -> torch.FloatTensor:
        """
493
        One step for the first-order DPMSolver (equivalent to DDIM).
494
495

        Args:
496
497
            model_output (`torch.FloatTensor`):
                The direct output from the learned diffusion model.
498
            sample (`torch.FloatTensor`):
499
                A current instance of a sample created by the diffusion process.
500
501

        Returns:
502
503
            `torch.FloatTensor`:
                The sample tensor at the previous timestep.
504
        """
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
        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)

532
533
534
535
536
        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
537
538
539
540
541
542
543
544
545
546
547
548
549
        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
550
551
552
            )
        return x_t

553
    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.multistep_dpm_solver_second_order_update
554
555
556
    def multistep_dpm_solver_second_order_update(
        self,
        model_output_list: List[torch.FloatTensor],
557
558
        *args,
        sample: torch.FloatTensor = None,
559
        noise: Optional[torch.FloatTensor] = None,
560
        **kwargs,
561
562
    ) -> torch.FloatTensor:
        """
563
        One step for the second-order multistep DPMSolver.
564
565
566

        Args:
            model_output_list (`List[torch.FloatTensor]`):
567
                The direct outputs from learned diffusion model at current and latter timesteps.
568
            sample (`torch.FloatTensor`):
569
                A current instance of a sample created by the diffusion process.
570
571

        Returns:
572
573
            `torch.FloatTensor`:
                The sample tensor at the previous timestep.
574
        """
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
        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)

610
        m0, m1 = model_output_list[-1], model_output_list[-2]
611

612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
        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
                )
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
        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
                )
675
676
677
678
679
680
        return x_t

    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.multistep_dpm_solver_third_order_update
    def multistep_dpm_solver_third_order_update(
        self,
        model_output_list: List[torch.FloatTensor],
681
682
683
        *args,
        sample: torch.FloatTensor = None,
        **kwargs,
684
685
    ) -> torch.FloatTensor:
        """
686
        One step for the third-order multistep DPMSolver.
687
688
689

        Args:
            model_output_list (`List[torch.FloatTensor]`):
690
                The direct outputs from learned diffusion model at current and latter timesteps.
691
            sample (`torch.FloatTensor`):
692
                A current instance of a sample created by diffusion process.
693
694

        Returns:
695
696
            `torch.FloatTensor`:
                The sample tensor at the previous timestep.
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

        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],
725
        )
726
727
728
729
730
731
732
733
734
735
736
737
738

        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]

739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
        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

763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._init_step_index
    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

    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.step
784
785
786
787
788
789
790
791
792
    def step(
        self,
        model_output: torch.FloatTensor,
        timestep: int,
        sample: torch.FloatTensor,
        generator=None,
        return_dict: bool = True,
    ) -> Union[SchedulerOutput, Tuple]:
        """
793
794
        Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
        the multistep DPMSolver.
795
796

        Args:
797
798
799
800
            model_output (`torch.FloatTensor`):
                The direct output from learned diffusion model.
            timestep (`int`):
                The current discrete timestep in the diffusion chain.
801
            sample (`torch.FloatTensor`):
802
                A current instance of a sample created by the diffusion process.
803
804
            generator (`torch.Generator`, *optional*):
                A random number generator.
805
806
            return_dict (`bool`):
                Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`.
807
808

        Returns:
809
810
811
            [`~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.
812
813
814
815
816
817
818

        """
        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"
            )

819
820
821
        if self.step_index is None:
            self._init_step_index(timestep)

822
823
824
        # Improve numerical stability for small number of steps
        lower_order_final = (self.step_index == len(self.timesteps) - 1) and (
            self.config.euler_at_final or (self.config.lower_order_final and len(self.timesteps) < 15)
825
826
        )
        lower_order_second = (
827
            (self.step_index == len(self.timesteps) - 2) and self.config.lower_order_final and len(self.timesteps) < 15
828
829
        )

830
        model_output = self.convert_model_output(model_output, sample=sample)
831
832
833
834
835
836
837
838
839
840
841
842
        for i in range(self.config.solver_order - 1):
            self.model_outputs[i] = self.model_outputs[i + 1]
        self.model_outputs[-1] = model_output

        if self.config.algorithm_type in ["sde-dpmsolver", "sde-dpmsolver++"]:
            noise = randn_tensor(
                model_output.shape, generator=generator, device=model_output.device, dtype=model_output.dtype
            )
        else:
            noise = None

        if self.config.solver_order == 1 or self.lower_order_nums < 1 or lower_order_final:
843
            prev_sample = self.dpm_solver_first_order_update(model_output, sample=sample, noise=noise)
844
        elif self.config.solver_order == 2 or self.lower_order_nums < 2 or lower_order_second:
845
            prev_sample = self.multistep_dpm_solver_second_order_update(self.model_outputs, sample=sample, noise=noise)
846
        else:
847
            prev_sample = self.multistep_dpm_solver_third_order_update(self.model_outputs, sample=sample)
848
849
850
851

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

852
853
854
        # upon completion increase step index by one
        self._step_index += 1

855
856
857
858
859
860
861
862
863
864
865
866
        if not return_dict:
            return (prev_sample,)

        return SchedulerOutput(prev_sample=prev_sample)

    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.scale_model_input
    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:
867
868
            sample (`torch.FloatTensor`):
                The input sample.
869
870

        Returns:
871
872
            `torch.FloatTensor`:
                A scaled input sample.
873
874
875
        """
        return sample

876
    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.add_noise
877
878
879
880
    def add_noise(
        self,
        original_samples: torch.FloatTensor,
        noise: torch.FloatTensor,
881
        timesteps: torch.IntTensor,
882
    ) -> torch.FloatTensor:
883
884
885
886
887
888
889
890
891
        # 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)
892

893
        step_indices = [(schedule_timesteps == t).nonzero().item() for t in timesteps]
894

895
896
897
        sigma = sigmas[step_indices].flatten()
        while len(sigma.shape) < len(original_samples.shape):
            sigma = sigma.unsqueeze(-1)
898

899
900
        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
        noisy_samples = alpha_t * original_samples + sigma_t * noise
901
902
903
904
        return noisy_samples

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