476 lines
21 KiB
Python
476 lines
21 KiB
Python
# Copyright 2025 Zhejiang University Team and The HuggingFace Team. All rights reserved.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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# DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim
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import math
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from typing import List, Optional, Tuple, Union
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import numpy as np
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import torch
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from ..configuration_utils import ConfigMixin, register_to_config
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from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
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# Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar
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def betas_for_alpha_bar(
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num_diffusion_timesteps,
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max_beta=0.999,
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alpha_transform_type="cosine",
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):
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"""
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Create a beta schedule that discretizes the given alpha_t_bar function, which defines the cumulative product of
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(1-beta) over time from t = [0,1].
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Contains a function alpha_bar that takes an argument t and transforms it to the cumulative product of (1-beta) up
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to that part of the diffusion process.
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Args:
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num_diffusion_timesteps (`int`): the number of betas to produce.
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max_beta (`float`): the maximum beta to use; use values lower than 1 to
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prevent singularities.
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alpha_transform_type (`str`, *optional*, default to `cosine`): the type of noise schedule for alpha_bar.
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Choose from `cosine` or `exp`
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Returns:
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betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
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"""
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if alpha_transform_type == "cosine":
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def alpha_bar_fn(t):
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return math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2
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elif alpha_transform_type == "exp":
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def alpha_bar_fn(t):
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return math.exp(t * -12.0)
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else:
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raise ValueError(f"Unsupported alpha_transform_type: {alpha_transform_type}")
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betas = []
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for i in range(num_diffusion_timesteps):
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t1 = i / num_diffusion_timesteps
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t2 = (i + 1) / num_diffusion_timesteps
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betas.append(min(1 - alpha_bar_fn(t2) / alpha_bar_fn(t1), max_beta))
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return torch.tensor(betas, dtype=torch.float32)
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class PNDMScheduler(SchedulerMixin, ConfigMixin):
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"""
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`PNDMScheduler` uses pseudo numerical methods for diffusion models such as the Runge-Kutta and linear multi-step
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method.
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This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
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methods the library implements for all schedulers such as loading and saving.
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Args:
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num_train_timesteps (`int`, defaults to 1000):
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The number of diffusion steps to train the model.
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beta_start (`float`, defaults to 0.0001):
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The starting `beta` value of inference.
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beta_end (`float`, defaults to 0.02):
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The final `beta` value.
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beta_schedule (`str`, defaults to `"linear"`):
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The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
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`linear`, `scaled_linear`, or `squaredcos_cap_v2`.
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trained_betas (`np.ndarray`, *optional*):
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Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
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skip_prk_steps (`bool`, defaults to `False`):
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Allows the scheduler to skip the Runge-Kutta steps defined in the original paper as being required before
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PLMS steps.
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set_alpha_to_one (`bool`, defaults to `False`):
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Each diffusion step uses the alphas product value at that step and at the previous one. For the final step
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there is no previous alpha. When this option is `True` the previous alpha product is fixed to `1`,
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otherwise it uses the alpha value at step 0.
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prediction_type (`str`, defaults to `epsilon`, *optional*):
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Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process)
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or `v_prediction` (see section 2.4 of [Imagen Video](https://imagen.research.google/video/paper.pdf)
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paper).
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timestep_spacing (`str`, defaults to `"leading"`):
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The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
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Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
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steps_offset (`int`, defaults to 0):
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An offset added to the inference steps, as required by some model families.
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"""
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_compatibles = [e.name for e in KarrasDiffusionSchedulers]
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order = 1
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@register_to_config
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def __init__(
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self,
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num_train_timesteps: int = 1000,
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beta_start: float = 0.0001,
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beta_end: float = 0.02,
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beta_schedule: str = "linear",
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trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
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skip_prk_steps: bool = False,
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set_alpha_to_one: bool = False,
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prediction_type: str = "epsilon",
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timestep_spacing: str = "leading",
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steps_offset: int = 0,
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):
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if trained_betas is not None:
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self.betas = torch.tensor(trained_betas, dtype=torch.float32)
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elif beta_schedule == "linear":
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self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32)
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elif beta_schedule == "scaled_linear":
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# this schedule is very specific to the latent diffusion model.
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self.betas = torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2
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elif beta_schedule == "squaredcos_cap_v2":
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# Glide cosine schedule
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self.betas = betas_for_alpha_bar(num_train_timesteps)
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else:
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raise NotImplementedError(f"{beta_schedule} is not implemented for {self.__class__}")
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self.alphas = 1.0 - self.betas
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self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
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self.final_alpha_cumprod = torch.tensor(1.0) if set_alpha_to_one else self.alphas_cumprod[0]
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# standard deviation of the initial noise distribution
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self.init_noise_sigma = 1.0
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# For now we only support F-PNDM, i.e. the runge-kutta method
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# For more information on the algorithm please take a look at the paper: https://huggingface.co/papers/2202.09778
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# mainly at formula (9), (12), (13) and the Algorithm 2.
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self.pndm_order = 4
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# running values
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self.cur_model_output = 0
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self.counter = 0
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self.cur_sample = None
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self.ets = []
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# setable values
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self.num_inference_steps = None
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self._timesteps = np.arange(0, num_train_timesteps)[::-1].copy()
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self.prk_timesteps = None
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self.plms_timesteps = None
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self.timesteps = None
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def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
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"""
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Sets the discrete timesteps used for the diffusion chain (to be run before inference).
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Args:
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num_inference_steps (`int`):
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The number of diffusion steps used when generating samples with a pre-trained model.
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device (`str` or `torch.device`, *optional*):
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The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
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"""
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self.num_inference_steps = num_inference_steps
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# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://huggingface.co/papers/2305.08891
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if self.config.timestep_spacing == "linspace":
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self._timesteps = (
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np.linspace(0, self.config.num_train_timesteps - 1, num_inference_steps).round().astype(np.int64)
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)
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elif self.config.timestep_spacing == "leading":
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step_ratio = self.config.num_train_timesteps // self.num_inference_steps
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# creates integer timesteps by multiplying by ratio
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# casting to int to avoid issues when num_inference_step is power of 3
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self._timesteps = (np.arange(0, num_inference_steps) * step_ratio).round()
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self._timesteps += self.config.steps_offset
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elif self.config.timestep_spacing == "trailing":
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step_ratio = self.config.num_train_timesteps / self.num_inference_steps
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# creates integer timesteps by multiplying by ratio
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# casting to int to avoid issues when num_inference_step is power of 3
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self._timesteps = np.round(np.arange(self.config.num_train_timesteps, 0, -step_ratio))[::-1].astype(
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np.int64
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)
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self._timesteps -= 1
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else:
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raise ValueError(
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f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."
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)
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if self.config.skip_prk_steps:
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# for some models like stable diffusion the prk steps can/should be skipped to
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# produce better results. When using PNDM with `self.config.skip_prk_steps` the implementation
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# is based on crowsonkb's PLMS sampler implementation: https://github.com/CompVis/latent-diffusion/pull/51
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self.prk_timesteps = np.array([])
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self.plms_timesteps = np.concatenate([self._timesteps[:-1], self._timesteps[-2:-1], self._timesteps[-1:]])[
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::-1
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].copy()
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else:
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prk_timesteps = np.array(self._timesteps[-self.pndm_order :]).repeat(2) + np.tile(
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np.array([0, self.config.num_train_timesteps // num_inference_steps // 2]), self.pndm_order
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)
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self.prk_timesteps = (prk_timesteps[:-1].repeat(2)[1:-1])[::-1].copy()
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self.plms_timesteps = self._timesteps[:-3][
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::-1
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].copy() # we copy to avoid having negative strides which are not supported by torch.from_numpy
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timesteps = np.concatenate([self.prk_timesteps, self.plms_timesteps]).astype(np.int64)
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self.timesteps = torch.from_numpy(timesteps).to(device)
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self.ets = []
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self.counter = 0
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self.cur_model_output = 0
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def step(
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self,
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model_output: torch.Tensor,
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timestep: int,
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sample: torch.Tensor,
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return_dict: bool = True,
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) -> Union[SchedulerOutput, Tuple]:
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"""
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Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
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process from the learned model outputs (most often the predicted noise), and calls [`~PNDMScheduler.step_prk`]
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or [`~PNDMScheduler.step_plms`] depending on the internal variable `counter`.
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Args:
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model_output (`torch.Tensor`):
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The direct output from learned diffusion model.
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timestep (`int`):
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The current discrete timestep in the diffusion chain.
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sample (`torch.Tensor`):
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A current instance of a sample created by the diffusion process.
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return_dict (`bool`):
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Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`.
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Returns:
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[`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
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If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a
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tuple is returned where the first element is the sample tensor.
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"""
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if self.counter < len(self.prk_timesteps) and not self.config.skip_prk_steps:
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return self.step_prk(model_output=model_output, timestep=timestep, sample=sample, return_dict=return_dict)
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else:
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return self.step_plms(model_output=model_output, timestep=timestep, sample=sample, return_dict=return_dict)
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def step_prk(
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self,
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model_output: torch.Tensor,
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timestep: int,
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sample: torch.Tensor,
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return_dict: bool = True,
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) -> Union[SchedulerOutput, Tuple]:
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"""
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Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
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the Runge-Kutta method. It performs four forward passes to approximate the solution to the differential
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equation.
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Args:
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model_output (`torch.Tensor`):
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The direct output from learned diffusion model.
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timestep (`int`):
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The current discrete timestep in the diffusion chain.
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sample (`torch.Tensor`):
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A current instance of a sample created by the diffusion process.
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return_dict (`bool`):
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Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or tuple.
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Returns:
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[`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
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If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a
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tuple is returned where the first element is the sample tensor.
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"""
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if self.num_inference_steps is None:
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raise ValueError(
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"Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
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)
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diff_to_prev = 0 if self.counter % 2 else self.config.num_train_timesteps // self.num_inference_steps // 2
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prev_timestep = timestep - diff_to_prev
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timestep = self.prk_timesteps[self.counter // 4 * 4]
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if self.counter % 4 == 0:
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self.cur_model_output += 1 / 6 * model_output
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self.ets.append(model_output)
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self.cur_sample = sample
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elif (self.counter - 1) % 4 == 0:
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self.cur_model_output += 1 / 3 * model_output
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elif (self.counter - 2) % 4 == 0:
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self.cur_model_output += 1 / 3 * model_output
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elif (self.counter - 3) % 4 == 0:
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model_output = self.cur_model_output + 1 / 6 * model_output
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self.cur_model_output = 0
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# cur_sample should not be `None`
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cur_sample = self.cur_sample if self.cur_sample is not None else sample
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prev_sample = self._get_prev_sample(cur_sample, timestep, prev_timestep, model_output)
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self.counter += 1
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if not return_dict:
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return (prev_sample,)
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return SchedulerOutput(prev_sample=prev_sample)
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def step_plms(
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self,
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model_output: torch.Tensor,
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timestep: int,
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sample: torch.Tensor,
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return_dict: bool = True,
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) -> Union[SchedulerOutput, Tuple]:
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"""
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Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
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the linear multistep method. It performs one forward pass multiple times to approximate the solution.
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Args:
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model_output (`torch.Tensor`):
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The direct output from learned diffusion model.
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timestep (`int`):
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The current discrete timestep in the diffusion chain.
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sample (`torch.Tensor`):
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A current instance of a sample created by the diffusion process.
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return_dict (`bool`):
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Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or tuple.
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Returns:
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[`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
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If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a
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tuple is returned where the first element is the sample tensor.
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"""
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if self.num_inference_steps is None:
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raise ValueError(
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"Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
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)
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if not self.config.skip_prk_steps and len(self.ets) < 3:
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raise ValueError(
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f"{self.__class__} can only be run AFTER scheduler has been run "
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"in 'prk' mode for at least 12 iterations "
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"See: https://github.com/huggingface/diffusers/blob/main/src/diffusers/pipelines/pipeline_pndm.py "
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"for more information."
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)
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prev_timestep = timestep - self.config.num_train_timesteps // self.num_inference_steps
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if self.counter != 1:
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self.ets = self.ets[-3:]
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self.ets.append(model_output)
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else:
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prev_timestep = timestep
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timestep = timestep + self.config.num_train_timesteps // self.num_inference_steps
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if len(self.ets) == 1 and self.counter == 0:
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model_output = model_output
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self.cur_sample = sample
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elif len(self.ets) == 1 and self.counter == 1:
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model_output = (model_output + self.ets[-1]) / 2
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sample = self.cur_sample
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self.cur_sample = None
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elif len(self.ets) == 2:
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model_output = (3 * self.ets[-1] - self.ets[-2]) / 2
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elif len(self.ets) == 3:
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model_output = (23 * self.ets[-1] - 16 * self.ets[-2] + 5 * self.ets[-3]) / 12
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else:
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model_output = (1 / 24) * (55 * self.ets[-1] - 59 * self.ets[-2] + 37 * self.ets[-3] - 9 * self.ets[-4])
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prev_sample = self._get_prev_sample(sample, timestep, prev_timestep, model_output)
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self.counter += 1
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if not return_dict:
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return (prev_sample,)
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return SchedulerOutput(prev_sample=prev_sample)
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def scale_model_input(self, sample: torch.Tensor, *args, **kwargs) -> torch.Tensor:
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"""
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Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
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current timestep.
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Args:
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sample (`torch.Tensor`):
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The input sample.
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Returns:
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`torch.Tensor`:
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A scaled input sample.
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"""
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return sample
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def _get_prev_sample(self, sample, timestep, prev_timestep, model_output):
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# See formula (9) of PNDM paper https://huggingface.co/papers/2202.09778
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# this function computes x_(t−δ) using the formula of (9)
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# Note that x_t needs to be added to both sides of the equation
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# Notation (<variable name> -> <name in paper>
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# alpha_prod_t -> α_t
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# alpha_prod_t_prev -> α_(t−δ)
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# beta_prod_t -> (1 - α_t)
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# beta_prod_t_prev -> (1 - α_(t−δ))
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# sample -> x_t
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# model_output -> e_θ(x_t, t)
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# prev_sample -> x_(t−δ)
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alpha_prod_t = self.alphas_cumprod[timestep]
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alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
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beta_prod_t = 1 - alpha_prod_t
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beta_prod_t_prev = 1 - alpha_prod_t_prev
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if self.config.prediction_type == "v_prediction":
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model_output = (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
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elif self.config.prediction_type != "epsilon":
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raise ValueError(
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f"prediction_type given as {self.config.prediction_type} must be one of `epsilon` or `v_prediction`"
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)
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||
# corresponds to (α_(t−δ) - α_t) divided by
|
||
# denominator of x_t in formula (9) and plus 1
|
||
# Note: (α_(t−δ) - α_t) / (sqrt(α_t) * (sqrt(α_(t−δ)) + sqr(α_t))) =
|
||
# sqrt(α_(t−δ)) / sqrt(α_t))
|
||
sample_coeff = (alpha_prod_t_prev / alpha_prod_t) ** (0.5)
|
||
|
||
# corresponds to denominator of e_θ(x_t, t) in formula (9)
|
||
model_output_denom_coeff = alpha_prod_t * beta_prod_t_prev ** (0.5) + (
|
||
alpha_prod_t * beta_prod_t * alpha_prod_t_prev
|
||
) ** (0.5)
|
||
|
||
# full formula (9)
|
||
prev_sample = (
|
||
sample_coeff * sample - (alpha_prod_t_prev - alpha_prod_t) * model_output / model_output_denom_coeff
|
||
)
|
||
|
||
return prev_sample
|
||
|
||
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.add_noise
|
||
def add_noise(
|
||
self,
|
||
original_samples: torch.Tensor,
|
||
noise: torch.Tensor,
|
||
timesteps: torch.IntTensor,
|
||
) -> torch.Tensor:
|
||
# Make sure alphas_cumprod and timestep have same device and dtype as original_samples
|
||
# Move the self.alphas_cumprod to device to avoid redundant CPU to GPU data movement
|
||
# for the subsequent add_noise calls
|
||
self.alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device)
|
||
alphas_cumprod = self.alphas_cumprod.to(dtype=original_samples.dtype)
|
||
timesteps = timesteps.to(original_samples.device)
|
||
|
||
sqrt_alpha_prod = alphas_cumprod[timesteps] ** 0.5
|
||
sqrt_alpha_prod = sqrt_alpha_prod.flatten()
|
||
while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
|
||
sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)
|
||
|
||
sqrt_one_minus_alpha_prod = (1 - alphas_cumprod[timesteps]) ** 0.5
|
||
sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
|
||
while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape):
|
||
sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)
|
||
|
||
noisy_samples = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
|
||
return noisy_samples
|
||
|
||
def __len__(self):
|
||
return self.config.num_train_timesteps
|