scheduling_ddpm.py

# Copyright 2022 UC Berkely Team and The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

# DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim

import math
from typing import Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import SchedulerMixin, SchedulerOutput


def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999):
    """
    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.

    Returns:
        betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
    """

    def alpha_bar(time_step):
        return math.cos((time_step + 0.008) / 1.008 * math.pi / 2) ** 2

    betas = []
    for i in range(num_diffusion_timesteps):
        t1 = i / num_diffusion_timesteps
        t2 = (i + 1) / num_diffusion_timesteps
        betas.append(min(1 - alpha_bar(t2) / alpha_bar(t1), max_beta))
    return np.array(betas, dtype=np.float32)


class DDPMScheduler(SchedulerMixin, ConfigMixin):
    """
    Denoising diffusion probabilistic models (DDPMs) explores the connections between denoising score matching and
    Langevin dynamics sampling.

    For more details, see the original paper: https://arxiv.org/abs/2006.11239

    Args:
        num_train_timesteps (`int`): number of diffusion steps used to train the model.
        beta_start (`float`): the starting `beta` value of inference.
        beta_end (`float`): the final `beta` value.
        beta_schedule (`str`):
            the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
            `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
        trained_betas (`np.ndarray`, optional): TODO
        variance_type (`str`):
            options to clip the variance used when adding noise to the denoised sample. Choose from `fixed_small`,
            `fixed_small_log`, `fixed_large`, `fixed_large_log`, `learned` or `learned_range`.
        clip_sample (`bool`, default `True`):
            option to clip predicted sample between -1 and 1 for numerical stability.
        tensor_format (`str`): whether the scheduler expects pytorch or numpy arrays.

    """

    @register_to_config
    def __init__(
        self,
        num_train_timesteps: int = 1000,
        beta_start: float = 0.0001,
        beta_end: float = 0.02,
        beta_schedule: str = "linear",
        trained_betas: Optional[np.ndarray] = None,
        variance_type: str = "fixed_small",
        clip_sample: bool = True,
        tensor_format: str = "pt",
    ):

        if trained_betas is not None:
            self.betas = np.asarray(trained_betas)
        elif beta_schedule == "linear":
            self.betas = np.linspace(beta_start, beta_end, num_train_timesteps, dtype=np.float32)
        elif beta_schedule == "scaled_linear":
            # this schedule is very specific to the latent diffusion model.
            self.betas = np.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=np.float32) ** 2
        elif beta_schedule == "squaredcos_cap_v2":
            # Glide cosine schedule
            self.betas = betas_for_alpha_bar(num_train_timesteps)
        else:
            raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}")

        self.alphas = 1.0 - self.betas
        self.alphas_cumprod = np.cumprod(self.alphas, axis=0)
        self.one = np.array(1.0)

        # setable values
        self.num_inference_steps = None
        self.timesteps = np.arange(0, num_train_timesteps)[::-1].copy()

        self.tensor_format = tensor_format
        self.set_format(tensor_format=tensor_format)

        self.variance_type = variance_type

    def set_timesteps(self, num_inference_steps: int):
        """
        Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.

        Args:
            num_inference_steps (`int`):
                the number of diffusion steps used when generating samples with a pre-trained model.
        """
        num_inference_steps = min(self.config.num_train_timesteps, num_inference_steps)
        self.num_inference_steps = num_inference_steps
        self.timesteps = np.arange(
            0, self.config.num_train_timesteps, self.config.num_train_timesteps // self.num_inference_steps
        )[::-1].copy()
        self.set_format(tensor_format=self.tensor_format)

    def _get_variance(self, t, predicted_variance=None, variance_type=None):
        alpha_prod_t = self.alphas_cumprod[t]
        alpha_prod_t_prev = self.alphas_cumprod[t - 1] if t > 0 else self.one

        # For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
        # and sample from it to get previous sample
        # x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
        variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * self.betas[t]

        if variance_type is None:
            variance_type = self.config.variance_type

        # hacks - were probs added for training stability
        if variance_type == "fixed_small":
            variance = self.clip(variance, min_value=1e-20)
        # for rl-diffuser https://arxiv.org/abs/2205.09991
        elif variance_type == "fixed_small_log":
            variance = self.log(self.clip(variance, min_value=1e-20))
        elif variance_type == "fixed_large":
            variance = self.betas[t]
        elif variance_type == "fixed_large_log":
            # Glide max_log
            variance = self.log(self.betas[t])
        elif variance_type == "learned":
            return predicted_variance
        elif variance_type == "learned_range":
            min_log = variance
            max_log = self.betas[t]
            frac = (predicted_variance + 1) / 2
            variance = frac * max_log + (1 - frac) * min_log

        return variance

    def step(
        self,
        model_output: Union[torch.FloatTensor, np.ndarray],
        timestep: int,
        sample: Union[torch.FloatTensor, np.ndarray],
        predict_epsilon=True,
        generator=None,
        return_dict: bool = True,
    ) -> Union[SchedulerOutput, Tuple]:
        """
        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
        process from the learned model outputs (most often the predicted noise).

        Args:
            model_output (`torch.FloatTensor` or `np.ndarray`): direct output from learned diffusion model.
            timestep (`int`): current discrete timestep in the diffusion chain.
            sample (`torch.FloatTensor` or `np.ndarray`):
                current instance of sample being created by diffusion process.
            eta (`float`): weight of noise for added noise in diffusion step.
            predict_epsilon (`bool`):
                optional flag to use when model predicts the samples directly instead of the noise, epsilon.
            generator: random number generator.
            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class

        Returns:
            `SchedulerOutput`: updated sample in the diffusion chain.

        """
        t = timestep

        if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]:
            model_output, predicted_variance = torch.split(model_output, sample.shape[1], dim=1)
        else:
            predicted_variance = None

        # 1. compute alphas, betas
        alpha_prod_t = self.alphas_cumprod[t]
        alpha_prod_t_prev = self.alphas_cumprod[t - 1] if t > 0 else self.one
        beta_prod_t = 1 - alpha_prod_t
        beta_prod_t_prev = 1 - alpha_prod_t_prev

        # 2. compute predicted original sample from predicted noise also called
        # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
        if predict_epsilon:
            pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
        else:
            pred_original_sample = model_output

        # 3. Clip "predicted x_0"
        if self.config.clip_sample:
            pred_original_sample = self.clip(pred_original_sample, -1, 1)

        # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
        # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
        pred_original_sample_coeff = (alpha_prod_t_prev ** (0.5) * self.betas[t]) / beta_prod_t
        current_sample_coeff = self.alphas[t] ** (0.5) * beta_prod_t_prev / beta_prod_t

        # 5. Compute predicted previous sample µ_t
        # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
        pred_prev_sample = pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

        # 6. Add noise
        variance = 0
        if t > 0:
            noise = self.randn_like(model_output, generator=generator)
            variance = (self._get_variance(t, predicted_variance=predicted_variance) ** 0.5) * noise

        pred_prev_sample = pred_prev_sample + variance

        if not return_dict:
            return (pred_prev_sample,)

        return SchedulerOutput(prev_sample=pred_prev_sample)

    def add_noise(
        self,
        original_samples: Union[torch.FloatTensor, np.ndarray],
        noise: Union[torch.FloatTensor, np.ndarray],
        timesteps: Union[torch.IntTensor, np.ndarray],
    ) -> Union[torch.FloatTensor, np.ndarray]:

        sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5
        sqrt_alpha_prod = self.match_shape(sqrt_alpha_prod, original_samples)
        sqrt_one_minus_alpha_prod = (1 - self.alphas_cumprod[timesteps]) ** 0.5
        sqrt_one_minus_alpha_prod = self.match_shape(sqrt_one_minus_alpha_prod, original_samples)

        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