scheduling_euler_discrete.py 24.7 KB
Newer Older
1
# Copyright 2024 Katherine Crowson and The HuggingFace Team. All rights reserved.
hlky's avatar
hlky committed
2
3
4
5
6
7
8
9
10
11
12
13
14
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

15
import math
hlky's avatar
hlky committed
16
from dataclasses import dataclass
17
from typing import List, Optional, Tuple, Union
hlky's avatar
hlky committed
18
19
20
21
22

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
Dhruv Nair's avatar
Dhruv Nair committed
23
24
from ..utils import BaseOutput, logging
from ..utils.torch_utils import randn_tensor
Kashif Rasul's avatar
Kashif Rasul committed
25
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
hlky's avatar
hlky committed
26
27
28
29
30
31
32
33
34


logger = logging.get_logger(__name__)  # pylint: disable=invalid-name


@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class EulerDiscreteSchedulerOutput(BaseOutput):
    """
35
    Output class for the scheduler's `step` function output.
hlky's avatar
hlky committed
36
37
38

    Args:
        prev_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
39
            Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the
hlky's avatar
hlky committed
40
41
            denoising loop.
        pred_original_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
42
            The predicted denoised sample `(x_{0})` based on the model output from the current timestep.
hlky's avatar
hlky committed
43
44
45
46
47
48
49
            `pred_original_sample` can be used to preview progress or for guidance.
    """

    prev_sample: torch.FloatTensor
    pred_original_sample: Optional[torch.FloatTensor] = None


50
# Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar
YiYi Xu's avatar
YiYi Xu committed
51
52
53
54
55
def betas_for_alpha_bar(
    num_diffusion_timesteps,
    max_beta=0.999,
    alpha_transform_type="cosine",
):
56
57
58
59
60
61
62
63
64
65
66
67
    """
    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
68
69
        alpha_transform_type (`str`, *optional*, default to `cosine`): the type of noise schedule for alpha_bar.
                     Choose from `cosine` or `exp`
70
71
72
73

    Returns:
        betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
    """
YiYi Xu's avatar
YiYi Xu committed
74
    if alpha_transform_type == "cosine":
75

YiYi Xu's avatar
YiYi Xu committed
76
77
78
79
80
81
82
83
84
85
        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}")
86
87
88
89
90

    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
91
        betas.append(min(1 - alpha_bar_fn(t2) / alpha_bar_fn(t1), max_beta))
92
93
94
    return torch.tensor(betas, dtype=torch.float32)


95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
# 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


hlky's avatar
hlky committed
132
133
class EulerDiscreteScheduler(SchedulerMixin, ConfigMixin):
    """
134
    Euler scheduler.
hlky's avatar
hlky committed
135

136
137
    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.
hlky's avatar
hlky committed
138
139

    Args:
140
141
142
143
144
145
146
147
        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
hlky's avatar
hlky committed
148
            `linear` or `scaled_linear`.
149
150
151
152
153
154
155
156
157
        trained_betas (`np.ndarray`, *optional*):
            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
        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).
        interpolation_type(`str`, defaults to `"linear"`, *optional*):
            The interpolation type to compute intermediate sigmas for the scheduler denoising steps. Should be on of
            `"linear"` or `"log_linear"`.
158
        use_karras_sigmas (`bool`, *optional*, defaults to `False`):
159
160
161
162
163
164
165
166
167
            Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If `True`,
            the sigmas are determined according to a sequence of noise levels {σi}.
        timestep_spacing (`str`, defaults to `"linspace"`):
            The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
            Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
        steps_offset (`int`, defaults to 0):
            An offset added to the inference steps. You can use a combination of `offset=1` and
            `set_alpha_to_one=False` to make the last step use step 0 for the previous alpha product like in Stable
            Diffusion.
168
169
170
171
        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).
hlky's avatar
hlky committed
172
173
    """

Kashif Rasul's avatar
Kashif Rasul committed
174
    _compatibles = [e.name for e in KarrasDiffusionSchedulers]
175
    order = 1
176

hlky's avatar
hlky committed
177
178
179
180
181
182
183
    @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",
184
        trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
Suraj Patil's avatar
Suraj Patil committed
185
        prediction_type: str = "epsilon",
186
        interpolation_type: str = "linear",
187
        use_karras_sigmas: Optional[bool] = False,
Suraj Patil's avatar
Suraj Patil committed
188
189
        sigma_min: Optional[float] = None,
        sigma_max: Optional[float] = None,
190
        timestep_spacing: str = "linspace",
Suraj Patil's avatar
Suraj Patil committed
191
        timestep_type: str = "discrete",  # can be "discrete" or "continuous"
192
        steps_offset: int = 0,
193
        rescale_betas_zero_snr: bool = False,
hlky's avatar
hlky committed
194
195
    ):
        if trained_betas is not None:
196
            self.betas = torch.tensor(trained_betas, dtype=torch.float32)
hlky's avatar
hlky committed
197
198
199
200
        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.
201
            self.betas = torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2
202
203
204
        elif beta_schedule == "squaredcos_cap_v2":
            # Glide cosine schedule
            self.betas = betas_for_alpha_bar(num_train_timesteps)
hlky's avatar
hlky committed
205
206
207
        else:
            raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}")

208
209
210
        if rescale_betas_zero_snr:
            self.betas = rescale_zero_terminal_snr(self.betas)

hlky's avatar
hlky committed
211
212
213
        self.alphas = 1.0 - self.betas
        self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)

214
215
216
217
218
        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

219
        sigmas = (((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5).flip(0)
Suraj Patil's avatar
Suraj Patil committed
220
221
        timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=float)[::-1].copy()
        timesteps = torch.from_numpy(timesteps).to(dtype=torch.float32)
hlky's avatar
hlky committed
222
223
224

        # setable values
        self.num_inference_steps = None
Suraj Patil's avatar
Suraj Patil committed
225
226
227
228
229
230
231
232
233

        # TODO: Support the full EDM scalings for all prediction types and timestep types
        if timestep_type == "continuous" and prediction_type == "v_prediction":
            self.timesteps = torch.Tensor([0.25 * sigma.log() for sigma in sigmas])
        else:
            self.timesteps = timesteps

        self.sigmas = torch.cat([sigmas, torch.zeros(1, device=sigmas.device)])

hlky's avatar
hlky committed
234
        self.is_scale_input_called = False
235
        self.use_karras_sigmas = use_karras_sigmas
hlky's avatar
hlky committed
236

YiYi Xu's avatar
YiYi Xu committed
237
        self._step_index = None
238
        self._begin_index = None
239
        self.sigmas = self.sigmas.to("cpu")  # to avoid too much CPU/GPU communication
YiYi Xu's avatar
YiYi Xu committed
240

241
242
243
    @property
    def init_noise_sigma(self):
        # standard deviation of the initial noise distribution
244
        max_sigma = max(self.sigmas) if isinstance(self.sigmas, list) else self.sigmas.max()
245
        if self.config.timestep_spacing in ["linspace", "trailing"]:
246
            return max_sigma
247

248
        return (max_sigma**2 + 1) ** 0.5
249

YiYi Xu's avatar
YiYi Xu committed
250
251
252
253
254
255
256
    @property
    def step_index(self):
        """
        The index counter for current timestep. It will increae 1 after each scheduler step.
        """
        return self._step_index

257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
    @property
    def begin_index(self):
        """
        The index for the first timestep. It should be set from pipeline with `set_begin_index` method.
        """
        return self._begin_index

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

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

hlky's avatar
hlky committed
275
276
277
278
    def scale_model_input(
        self, sample: torch.FloatTensor, timestep: Union[float, torch.FloatTensor]
    ) -> torch.FloatTensor:
        """
279
280
        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
        current timestep. Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the Euler algorithm.
hlky's avatar
hlky committed
281
282

        Args:
283
284
285
286
            sample (`torch.FloatTensor`):
                The input sample.
            timestep (`int`, *optional*):
                The current timestep in the diffusion chain.
hlky's avatar
hlky committed
287
288

        Returns:
289
290
            `torch.FloatTensor`:
                A scaled input sample.
hlky's avatar
hlky committed
291
        """
YiYi Xu's avatar
YiYi Xu committed
292
293
        if self.step_index is None:
            self._init_step_index(timestep)
294

YiYi Xu's avatar
YiYi Xu committed
295
        sigma = self.sigmas[self.step_index]
hlky's avatar
hlky committed
296
        sample = sample / ((sigma**2 + 1) ** 0.5)
297

hlky's avatar
hlky committed
298
299
300
301
302
        self.is_scale_input_called = True
        return sample

    def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
        """
303
        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
hlky's avatar
hlky committed
304
305
306

        Args:
            num_inference_steps (`int`):
307
308
309
                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.
hlky's avatar
hlky committed
310
311
312
        """
        self.num_inference_steps = num_inference_steps

313
314
        # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
        if self.config.timestep_spacing == "linspace":
YiYi Xu's avatar
YiYi Xu committed
315
            timesteps = np.linspace(0, self.config.num_train_timesteps - 1, num_inference_steps, dtype=np.float32)[
316
317
318
319
320
321
                ::-1
            ].copy()
        elif self.config.timestep_spacing == "leading":
            step_ratio = self.config.num_train_timesteps // self.num_inference_steps
            # creates integer timesteps by multiplying by ratio
            # casting to int to avoid issues when num_inference_step is power of 3
YiYi Xu's avatar
YiYi Xu committed
322
            timesteps = (np.arange(0, num_inference_steps) * step_ratio).round()[::-1].copy().astype(np.float32)
323
324
325
326
327
            timesteps += self.config.steps_offset
        elif self.config.timestep_spacing == "trailing":
            step_ratio = self.config.num_train_timesteps / self.num_inference_steps
            # creates integer timesteps by multiplying by ratio
            # casting to int to avoid issues when num_inference_step is power of 3
YiYi Xu's avatar
YiYi Xu committed
328
            timesteps = (np.arange(self.config.num_train_timesteps, 0, -step_ratio)).round().copy().astype(np.float32)
329
330
331
332
333
334
            timesteps -= 1
        else:
            raise ValueError(
                f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."
            )

hlky's avatar
hlky committed
335
        sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
336
        log_sigmas = np.log(sigmas)
337
338
339
340

        if self.config.interpolation_type == "linear":
            sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
        elif self.config.interpolation_type == "log_linear":
341
            sigmas = torch.linspace(np.log(sigmas[-1]), np.log(sigmas[0]), num_inference_steps + 1).exp().numpy()
342
343
344
345
346
347
        else:
            raise ValueError(
                f"{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either"
                " 'linear' or 'log_linear'"
            )

348
        if self.use_karras_sigmas:
349
            sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=self.num_inference_steps)
350
351
            timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])

Suraj Patil's avatar
Suraj Patil committed
352
        sigmas = torch.from_numpy(sigmas).to(dtype=torch.float32, device=device)
YiYi Xu's avatar
YiYi Xu committed
353

Suraj Patil's avatar
Suraj Patil committed
354
355
356
357
358
359
360
        # TODO: Support the full EDM scalings for all prediction types and timestep types
        if self.config.timestep_type == "continuous" and self.config.prediction_type == "v_prediction":
            self.timesteps = torch.Tensor([0.25 * sigma.log() for sigma in sigmas]).to(device=device)
        else:
            self.timesteps = torch.from_numpy(timesteps.astype(np.float32)).to(device=device)

        self.sigmas = torch.cat([sigmas, torch.zeros(1, device=sigmas.device)])
YiYi Xu's avatar
YiYi Xu committed
361
        self._step_index = None
362
        self._begin_index = None
363
        self.sigmas = self.sigmas.to("cpu")  # to avoid too much CPU/GPU communication
hlky's avatar
hlky committed
364

365
366
    def _sigma_to_t(self, sigma, log_sigmas):
        # get log sigma
367
        log_sigma = np.log(np.maximum(sigma, 1e-10))
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388

        # 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

    # Copied from https://github.com/crowsonkb/k-diffusion/blob/686dbad0f39640ea25c8a8c6a6e56bb40eacefa2/k_diffusion/sampling.py#L17
389
    def _convert_to_karras(self, in_sigmas: torch.FloatTensor, num_inference_steps) -> torch.FloatTensor:
390
391
        """Constructs the noise schedule of Karras et al. (2022)."""

Suraj Patil's avatar
Suraj Patil committed
392
393
394
395
396
397
398
399
400
401
402
403
404
405
        # 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()
406
407

        rho = 7.0  # 7.0 is the value used in the paper
408
        ramp = np.linspace(0, 1, num_inference_steps)
409
410
411
412
413
        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

414
415
416
    def index_for_timestep(self, timestep, schedule_timesteps=None):
        if schedule_timesteps is None:
            schedule_timesteps = self.timesteps
YiYi Xu's avatar
YiYi Xu committed
417

418
        indices = (schedule_timesteps == timestep).nonzero()
YiYi Xu's avatar
YiYi Xu committed
419
420
421
422
423

        # 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)
424
        pos = 1 if len(indices) > 1 else 0
YiYi Xu's avatar
YiYi Xu committed
425

426
427
428
429
430
431
432
433
434
        return indices[pos].item()

    def _init_step_index(self, timestep):
        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
YiYi Xu's avatar
YiYi Xu committed
435

hlky's avatar
hlky committed
436
437
438
439
440
441
442
443
444
445
446
447
448
    def step(
        self,
        model_output: torch.FloatTensor,
        timestep: Union[float, torch.FloatTensor],
        sample: torch.FloatTensor,
        s_churn: float = 0.0,
        s_tmin: float = 0.0,
        s_tmax: float = float("inf"),
        s_noise: float = 1.0,
        generator: Optional[torch.Generator] = None,
        return_dict: bool = True,
    ) -> Union[EulerDiscreteSchedulerOutput, Tuple]:
        """
449
        Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
hlky's avatar
hlky committed
450
451
452
        process from the learned model outputs (most often the predicted noise).

        Args:
453
454
455
456
            model_output (`torch.FloatTensor`):
                The direct output from learned diffusion model.
            timestep (`float`):
                The current discrete timestep in the diffusion chain.
hlky's avatar
hlky committed
457
            sample (`torch.FloatTensor`):
458
459
460
461
462
463
464
465
466
467
468
                A current instance of a sample created by the diffusion process.
            s_churn (`float`):
            s_tmin  (`float`):
            s_tmax  (`float`):
            s_noise (`float`, defaults to 1.0):
                Scaling factor for noise added to the sample.
            generator (`torch.Generator`, *optional*):
                A random number generator.
            return_dict (`bool`):
                Whether or not to return a [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] or
                tuple.
hlky's avatar
hlky committed
469
470

        Returns:
471
472
473
            [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] or `tuple`:
                If return_dict is `True`, [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] is
                returned, otherwise a tuple is returned where the first element is the sample tensor.
hlky's avatar
hlky committed
474
475
476
477
478
479
480
481
        """

        if (
            isinstance(timestep, int)
            or isinstance(timestep, torch.IntTensor)
            or isinstance(timestep, torch.LongTensor)
        ):
            raise ValueError(
Patrick von Platen's avatar
Patrick von Platen committed
482
483
484
485
486
                (
                    "Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
                    " `EulerDiscreteScheduler.step()` is not supported. Make sure to pass"
                    " one of the `scheduler.timesteps` as a timestep."
                ),
hlky's avatar
hlky committed
487
488
489
            )

        if not self.is_scale_input_called:
490
            logger.warning(
hlky's avatar
hlky committed
491
492
493
494
                "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
                "See `StableDiffusionPipeline` for a usage example."
            )

YiYi Xu's avatar
YiYi Xu committed
495
496
        if self.step_index is None:
            self._init_step_index(timestep)
hlky's avatar
hlky committed
497

498
499
500
        # Upcast to avoid precision issues when computing prev_sample
        sample = sample.to(torch.float32)

YiYi Xu's avatar
YiYi Xu committed
501
        sigma = self.sigmas[self.step_index]
hlky's avatar
hlky committed
502
503
504

        gamma = min(s_churn / (len(self.sigmas) - 1), 2**0.5 - 1) if s_tmin <= sigma <= s_tmax else 0.0

505
506
507
        noise = randn_tensor(
            model_output.shape, dtype=model_output.dtype, device=model_output.device, generator=generator
        )
508

hlky's avatar
hlky committed
509
510
511
512
513
514
515
        eps = noise * s_noise
        sigma_hat = sigma * (gamma + 1)

        if gamma > 0:
            sample = sample + eps * (sigma_hat**2 - sigma**2) ** 0.5

        # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
516
517
518
        # NOTE: "original_sample" should not be an expected prediction_type but is left in for
        # backwards compatibility
        if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
519
520
            pred_original_sample = model_output
        elif self.config.prediction_type == "epsilon":
Suraj Patil's avatar
Suraj Patil committed
521
            pred_original_sample = sample - sigma_hat * model_output
522
        elif self.config.prediction_type == "v_prediction":
Suraj Patil's avatar
Suraj Patil committed
523
            # denoised = model_output * c_out + input * c_skip
Suraj Patil's avatar
Suraj Patil committed
524
525
526
            pred_original_sample = model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
        else:
            raise ValueError(
527
                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"
Suraj Patil's avatar
Suraj Patil committed
528
            )
hlky's avatar
hlky committed
529
530
531
532

        # 2. Convert to an ODE derivative
        derivative = (sample - pred_original_sample) / sigma_hat

YiYi Xu's avatar
YiYi Xu committed
533
        dt = self.sigmas[self.step_index + 1] - sigma_hat
hlky's avatar
hlky committed
534
535
536

        prev_sample = sample + derivative * dt

537
538
539
        # Cast sample back to model compatible dtype
        prev_sample = prev_sample.to(model_output.dtype)

YiYi Xu's avatar
YiYi Xu committed
540
541
542
        # upon completion increase step index by one
        self._step_index += 1

hlky's avatar
hlky committed
543
544
545
546
547
548
549
550
551
552
553
554
        if not return_dict:
            return (prev_sample,)

        return EulerDiscreteSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_sample)

    def add_noise(
        self,
        original_samples: torch.FloatTensor,
        noise: torch.FloatTensor,
        timesteps: torch.FloatTensor,
    ) -> torch.FloatTensor:
        # Make sure sigmas and timesteps have the same device and dtype as original_samples
555
        sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
hlky's avatar
hlky committed
556
557
        if original_samples.device.type == "mps" and torch.is_floating_point(timesteps):
            # mps does not support float64
558
            schedule_timesteps = self.timesteps.to(original_samples.device, dtype=torch.float32)
hlky's avatar
hlky committed
559
560
            timesteps = timesteps.to(original_samples.device, dtype=torch.float32)
        else:
561
            schedule_timesteps = self.timesteps.to(original_samples.device)
hlky's avatar
hlky committed
562
563
            timesteps = timesteps.to(original_samples.device)

564
565
566
567
568
        # self.begin_index is None when scheduler is used for training, or pipeline does not implement set_begin_index
        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]
hlky's avatar
hlky committed
569

570
        sigma = sigmas[step_indices].flatten()
hlky's avatar
hlky committed
571
572
573
574
575
576
577
578
        while len(sigma.shape) < len(original_samples.shape):
            sigma = sigma.unsqueeze(-1)

        noisy_samples = original_samples + noise * sigma
        return noisy_samples

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