253 lines
10 KiB
Python
253 lines
10 KiB
Python
# Copyright 2022 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 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 SchedulerMixin
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def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999):
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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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:param num_diffusion_timesteps: the number of betas to produce. :param alpha_bar: a lambda that takes an argument t
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from 0 to 1 and
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produces the cumulative product of (1-beta) up to that part of the diffusion process.
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:param max_beta: the maximum beta to use; use values lower than 1 to
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prevent singularities.
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"""
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def alpha_bar(time_step):
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return math.cos((time_step + 0.008) / 1.008 * math.pi / 2) ** 2
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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(t2) / alpha_bar(t1), max_beta))
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return np.array(betas, dtype=np.float32)
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class PNDMScheduler(SchedulerMixin, ConfigMixin):
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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=1000,
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beta_start=0.0001,
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beta_end=0.02,
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beta_schedule="linear",
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tensor_format="pt",
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skip_prk_steps=False,
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):
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if beta_schedule == "linear":
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self.betas = np.linspace(beta_start, beta_end, num_train_timesteps, dtype=np.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 = np.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=np.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} does is not implemented for {self.__class__}")
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self.alphas = 1.0 - self.betas
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self.alphas_cumprod = np.cumprod(self.alphas, axis=0)
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self.one = np.array(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://arxiv.org/pdf/2202.09778.pdf
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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._offset = 0
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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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self.tensor_format = tensor_format
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self.set_format(tensor_format=tensor_format)
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def set_timesteps(self, num_inference_steps, offset=0):
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self.num_inference_steps = num_inference_steps
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self._timesteps = list(
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range(0, self.config.num_train_timesteps, self.config.num_train_timesteps // num_inference_steps)
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)
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self._offset = offset
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self._timesteps = [t + self._offset for t in self._timesteps]
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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 = []
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self.plms_timesteps = list(reversed(self._timesteps[:-1] + self._timesteps[-2:-1] + self._timesteps[-1:]))
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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 = list(reversed(prk_timesteps[:-1].repeat(2)[1:-1]))
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self.plms_timesteps = list(reversed(self._timesteps[:-3]))
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self.timesteps = self.prk_timesteps + self.plms_timesteps
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self.counter = 0
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self.set_format(tensor_format=self.tensor_format)
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def step(
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self,
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model_output: Union[torch.FloatTensor, np.ndarray],
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timestep: int,
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sample: Union[torch.FloatTensor, np.ndarray],
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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)
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else:
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return self.step_plms(model_output=model_output, timestep=timestep, sample=sample)
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def step_prk(
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self,
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model_output: Union[torch.FloatTensor, np.ndarray],
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timestep: int,
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sample: Union[torch.FloatTensor, np.ndarray],
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):
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"""
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Step function propagating the sample with the Runge-Kutta method. RK takes 4 forward passes to approximate the
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solution to the differential equation.
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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 = max(timestep - diff_to_prev, self.prk_timesteps[-1])
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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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return {"prev_sample": prev_sample}
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def step_plms(
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self,
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model_output: Union[torch.FloatTensor, np.ndarray],
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timestep: int,
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sample: Union[torch.FloatTensor, np.ndarray],
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):
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"""
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Step function propagating the sample with the linear multi-step method. This has one forward pass with multiple
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times to approximate the solution.
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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 = max(timestep - self.config.num_train_timesteps // self.num_inference_steps, 0)
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if self.counter != 1:
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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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return {"prev_sample": prev_sample}
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def _get_prev_sample(self, sample, timestep, timestep_prev, model_output):
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# See formula (9) of PNDM paper https://arxiv.org/pdf/2202.09778.pdf
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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 + 1 - self._offset]
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alpha_prod_t_prev = self.alphas_cumprod[timestep_prev + 1 - self._offset]
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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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# corresponds to (α_(t−δ) - α_t) divided by
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# denominator of x_t in formula (9) and plus 1
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# Note: (α_(t−δ) - α_t) / (sqrt(α_t) * (sqrt(α_(t−δ)) + sqr(α_t))) =
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# sqrt(α_(t−δ)) / sqrt(α_t))
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sample_coeff = (alpha_prod_t_prev / alpha_prod_t) ** (0.5)
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# corresponds to denominator of e_θ(x_t, t) in formula (9)
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model_output_denom_coeff = alpha_prod_t * beta_prod_t_prev ** (0.5) + (
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alpha_prod_t * beta_prod_t * alpha_prod_t_prev
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) ** (0.5)
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# full formula (9)
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prev_sample = (
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sample_coeff * sample - (alpha_prod_t_prev - alpha_prod_t) * model_output / model_output_denom_coeff
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)
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return prev_sample
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def __len__(self):
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return self.config.num_train_timesteps
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