scheduling_pndm.py

# Copyright 2022 Zhejiang University 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 Union

import numpy as np
import torch

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


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].

    :param num_diffusion_timesteps: the number of betas to produce. :param alpha_bar: a lambda that takes an argument t
    from 0 to 1 and
                      produces the cumulative product of (1-beta) up to that part of the diffusion process.
    :param max_beta: the maximum beta to use; use values lower than 1 to
                     prevent singularities.
    """

    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 PNDMScheduler(SchedulerMixin, ConfigMixin):
    @register_to_config
    def __init__(
        self,
        num_train_timesteps=1000,
        beta_start=0.0001,
        beta_end=0.02,
        beta_schedule="linear",
        tensor_format="pt",
    ):

        if 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)

        # For now we only support F-PNDM, i.e. the runge-kutta method
        # For more information on the algorithm please take a look at the paper: https://arxiv.org/pdf/2202.09778.pdf
        # mainly at formula (9), (12), (13) and the Algorithm 2.
        self.pndm_order = 4

        # running values
        self.cur_model_output = 0
        self.counter = 0
        self.cur_sample = None
        self.ets = []

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

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

    def set_timesteps(self, num_inference_steps):
        self.num_inference_steps = num_inference_steps
        self._timesteps = list(
            range(0, self.config.num_train_timesteps, self.config.num_train_timesteps // num_inference_steps)
        )

        prk_timesteps = np.array(self._timesteps[-self.pndm_order :]).repeat(2) + np.tile(
            np.array([0, self.config.num_train_timesteps // num_inference_steps // 2]), self.pndm_order
        )
        self.prk_timesteps = list(reversed(prk_timesteps[:-1].repeat(2)[1:-1]))
        self.plms_timesteps = list(reversed(self._timesteps[:-3]))
        self.timesteps = self.prk_timesteps + self.plms_timesteps

        self.counter = 0
        self.set_format(tensor_format=self.tensor_format)

    def step(
        self,
        model_output: Union[torch.FloatTensor, np.ndarray],
        timestep: int,
        sample: Union[torch.FloatTensor, np.ndarray],
    ):
        if self.counter < len(self.prk_timesteps):
            return self.step_prk(model_output=model_output, timestep=timestep, sample=sample)
        else:
            return self.step_plms(model_output=model_output, timestep=timestep, sample=sample)

    def step_prk(
        self,
        model_output: Union[torch.FloatTensor, np.ndarray],
        timestep: int,
        sample: Union[torch.FloatTensor, np.ndarray],
    ):
        """
        Step function propagating the sample with the Runge-Kutta method. RK takes 4 forward passes to approximate the
        solution to the differential equation.
        """
        diff_to_prev = 0 if self.counter % 2 else self.config.num_train_timesteps // self.num_inference_steps // 2
        prev_timestep = max(timestep - diff_to_prev, self.prk_timesteps[-1])
        timestep = self.prk_timesteps[self.counter // 4 * 4]

        if self.counter % 4 == 0:
            self.cur_model_output += 1 / 6 * model_output
            self.ets.append(model_output)
            self.cur_sample = sample
        elif (self.counter - 1) % 4 == 0:
            self.cur_model_output += 1 / 3 * model_output
        elif (self.counter - 2) % 4 == 0:
            self.cur_model_output += 1 / 3 * model_output
        elif (self.counter - 3) % 4 == 0:
            model_output = self.cur_model_output + 1 / 6 * model_output
            self.cur_model_output = 0

        # cur_sample should not be `None`
        cur_sample = self.cur_sample if self.cur_sample is not None else sample

        prev_sample = self._get_prev_sample(cur_sample, timestep, prev_timestep, model_output)
        self.counter += 1

        return {"prev_sample": prev_sample}

    def step_plms(
        self,
        model_output: Union[torch.FloatTensor, np.ndarray],
        timestep: int,
        sample: Union[torch.FloatTensor, np.ndarray],
    ):
        """
        Step function propagating the sample with the linear multi-step method. This has one forward pass with multiple
        times to approximate the solution.
        """
        if len(self.ets) < 3:
            raise ValueError(
                f"{self.__class__} can only be run AFTER scheduler has been run "
                "in 'prk' mode for at least 12 iterations "
                "See: https://github.com/huggingface/diffusers/blob/main/src/diffusers/pipelines/pipeline_pndm.py "
                "for more information."
            )

        prev_timestep = max(timestep - self.config.num_train_timesteps // self.num_inference_steps, 0)
        self.ets.append(model_output)

        model_output = (1 / 24) * (55 * self.ets[-1] - 59 * self.ets[-2] + 37 * self.ets[-3] - 9 * self.ets[-4])

        prev_sample = self._get_prev_sample(sample, timestep, prev_timestep, model_output)
        self.counter += 1

        return {"prev_sample": prev_sample}

    def _get_prev_sample(self, sample, timestep, timestep_prev, model_output):
        # See formula (9) of PNDM paper https://arxiv.org/pdf/2202.09778.pdf
        # this function computes x_(t−δ) using the formula of (9)
        # Note that x_t needs to be added to both sides of the equation

        # Notation (<variable name> -> <name in paper>
        # alpha_prod_t -> α_t
        # alpha_prod_t_prev -> α_(t−δ)
        # beta_prod_t -> (1 - α_t)
        # beta_prod_t_prev -> (1 - α_(t−δ))
        # sample -> x_t
        # model_output -> e_θ(x_t, t)
        # prev_sample -> x_(t−δ)
        alpha_prod_t = self.alphas_cumprod[timestep + 1]
        alpha_prod_t_prev = self.alphas_cumprod[timestep_prev + 1]
        beta_prod_t = 1 - alpha_prod_t
        beta_prod_t_prev = 1 - alpha_prod_t_prev

        # 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

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