185 lines
7.8 KiB
Python
185 lines
7.8 KiB
Python
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# Copyright 2022 Stanford 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 code is strongly influenced by https://github.com/pesser/pytorch_diffusion
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# and https://github.com/hojonathanho/diffusion
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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 DDIMScheduler(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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trained_betas=None,
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timestep_values=None,
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clip_sample=True,
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set_alpha_to_one=True,
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tensor_format="pt",
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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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# At every step in ddim, we are looking into the previous alphas_cumprod
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# For the final step, there is no previous alphas_cumprod because we are already at 0
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# `set_alpha_to_one` decides whether we set this paratemer simply to one or
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# whether we use the final alpha of the "non-previous" one.
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self.final_alpha_cumprod = np.array(1.0) if set_alpha_to_one else self.alphas_cumprod[0]
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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.tensor_format = tensor_format
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self.set_format(tensor_format=tensor_format)
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def _get_variance(self, timestep, prev_timestep):
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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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variance = (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)
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return variance
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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 = np.arange(
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0, self.config.num_train_timesteps, self.config.num_train_timesteps // self.num_inference_steps
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)[::-1].copy()
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self.timesteps += offset
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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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eta: float = 0.0,
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use_clipped_model_output: bool = False,
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generator=None,
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):
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# See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
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# Ideally, read DDIM paper in-detail understanding
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# Notation (<variable name> -> <name in paper>
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# - pred_noise_t -> e_theta(x_t, t)
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# - pred_original_sample -> f_theta(x_t, t) or x_0
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# - std_dev_t -> sigma_t
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# - eta -> η
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# - pred_sample_direction -> "direction pointingc to x_t"
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# - pred_prev_sample -> "x_t-1"
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# 1. get previous step value (=t-1)
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prev_timestep = timestep - self.config.num_train_timesteps // self.num_inference_steps
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# 2. compute alphas, betas
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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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# 3. compute predicted original sample from predicted noise also called
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# "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
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pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
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# 4. Clip "predicted x_0"
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if self.config.clip_sample:
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pred_original_sample = self.clip(pred_original_sample, -1, 1)
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# 5. compute variance: "sigma_t(η)" -> see formula (16)
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# σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
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variance = self._get_variance(timestep, prev_timestep)
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std_dev_t = eta * variance ** (0.5)
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if use_clipped_model_output:
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# the model_output is always re-derived from the clipped x_0 in Glide
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model_output = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5)
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# 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
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pred_sample_direction = (1 - alpha_prod_t_prev - std_dev_t**2) ** (0.5) * model_output
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# 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
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prev_sample = alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_direction
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if eta > 0:
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device = model_output.device if torch.is_tensor(model_output) else "cpu"
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noise = torch.randn(model_output.shape, generator=generator).to(device)
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variance = self._get_variance(timestep, prev_timestep) ** (0.5) * eta * noise
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if not torch.is_tensor(model_output):
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variance = variance.numpy()
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prev_sample = prev_sample + variance
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return {"prev_sample": prev_sample}
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def add_noise(self, original_samples, noise, timesteps):
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sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5
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sqrt_alpha_prod = self.match_shape(sqrt_alpha_prod, original_samples)
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sqrt_one_minus_alpha_prod = (1 - self.alphas_cumprod[timesteps]) ** 0.5
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sqrt_one_minus_alpha_prod = self.match_shape(sqrt_one_minus_alpha_prod, original_samples)
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noisy_samples = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
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return noisy_samples
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def __len__(self):
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return self.config.num_train_timesteps
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