midi/schedulers/scheduling_rectified_flow.py

"""
Adapted from https://github.com/huggingface/diffusers/blob/v0.30.3/src/diffusers/schedulers/scheduling_flow_match_euler_discrete.py.
"""

import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch
from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.schedulers.scheduling_utils import SchedulerMixin
from diffusers.utils import BaseOutput, logging
from torch.distributions import LogisticNormal

logger = logging.get_logger(__name__)  # pylint: disable=invalid-name


# TODO: may move to training_utils.py
def compute_density_for_timestep_sampling(
    weighting_scheme: str,
    batch_size: int,
    logit_mean: float = 0.0,
    logit_std: float = 1.0,
    mode_scale: float = None,
):
    if weighting_scheme == "logit_normal":
        # See 3.1 in the SD3 paper ($rf/lognorm(0.00,1.00)$).
        u = torch.normal(
            mean=logit_mean, std=logit_std, size=(batch_size,), device="cpu"
        )
        u = torch.nn.functional.sigmoid(u)
    elif weighting_scheme == "logit_normal_dist":
        u = (
            LogisticNormal(loc=logit_mean, scale=logit_std)
            .sample((batch_size,))[:, 0]
            .to("cpu")
        )
    elif weighting_scheme == "mode":
        u = torch.rand(size=(batch_size,), device="cpu")
        u = 1 - u - mode_scale * (torch.cos(math.pi * u / 2) ** 2 - 1 + u)
    else:
        u = torch.rand(size=(batch_size,), device="cpu")
    return u


def compute_loss_weighting(weighting_scheme: str, sigmas=None):
    """
    Computes loss weighting scheme for SD3 training.

    Courtesy: This was contributed by Rafie Walker in https://github.com/huggingface/diffusers/pull/8528.

    SD3 paper reference: https://arxiv.org/abs/2403.03206v1.
    """
    if weighting_scheme == "sigma_sqrt":
        weighting = (sigmas**-2.0).float()
    elif weighting_scheme == "cosmap":
        bot = 1 - 2 * sigmas + 2 * sigmas**2
        weighting = 2 / (math.pi * bot)
    else:
        weighting = torch.ones_like(sigmas)
    return weighting


@dataclass
class RectifiedFlowSchedulerOutput(BaseOutput):
    """
    Output class for the scheduler's `step` function output.

    Args:
        prev_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
            Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the
            denoising loop.
    """

    prev_sample: torch.FloatTensor


class RectifiedFlowScheduler(SchedulerMixin, ConfigMixin):
    """
    The rectified flow scheduler is a scheduler that is used to propagate the diffusion process in the rectified flow.

    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
    methods the library implements for all schedulers such as loading and saving.

    Args:
        num_train_timesteps (`int`, defaults to 1000):
            The number of diffusion steps to train the model.
        timestep_spacing (`str`, defaults to `"linspace"`):
            The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
            Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
        shift (`float`, defaults to 1.0):
            The shift value for the timestep schedule.
    """

    _compatibles = []
    order = 1

    @register_to_config
    def __init__(
        self,
        num_train_timesteps: int = 1000,
        shift: float = 1.0,
        use_dynamic_shifting: bool = False,
    ):
        # pre-compute timesteps and sigmas; no use in fact
        # NOTE that shape diffusion sample timesteps randomly or in a distribution,
        # instead of sampling from the pre-defined linspace
        timesteps = np.array(
            [
                (1.0 - i / num_train_timesteps) * num_train_timesteps
                for i in range(num_train_timesteps)
            ]
        )
        timesteps = torch.from_numpy(timesteps).to(dtype=torch.float32)

        sigmas = timesteps / num_train_timesteps
        if not use_dynamic_shifting:
            # when use_dynamic_shifting is True, we apply the timestep shifting on the fly based on the image resolution
            sigmas = self.time_shift(sigmas)

        self.timesteps = sigmas * num_train_timesteps

        self._step_index = None
        self._begin_index = None

        self.sigmas = sigmas.to("cpu")  # to avoid too much CPU/GPU communication

    @property
    def step_index(self):
        """
        The index counter for current timestep. It will increase 1 after each scheduler step.
        """
        return self._step_index

    @property
    def begin_index(self):
        """
        The index for the first timestep. It should be set from pipeline with `set_begin_index` method.
        """
        return self._begin_index

    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.set_begin_index
    def set_begin_index(self, begin_index: int = 0):
        """
        Sets the begin index for the scheduler. This function should be run from pipeline before the inference.

        Args:
            begin_index (`int`):
                The begin index for the scheduler.
        """
        self._begin_index = begin_index

    def _sigma_to_t(self, sigma):
        return sigma * self.config.num_train_timesteps

    def _t_to_sigma(self, timestep):
        return timestep / self.config.num_train_timesteps

    def time_shift_dynamic(self, mu: float, sigma: float, t: torch.Tensor):
        return math.exp(mu) / (math.exp(mu) + (1 / t - 1) ** sigma)

    def time_shift(self, t: torch.Tensor):
        return self.config.shift * t / (1 + (self.config.shift - 1) * t)

    def set_timesteps(
        self,
        num_inference_steps: int = None,
        device: Union[str, torch.device] = None,
        sigmas: Optional[List[float]] = None,
        mu: Optional[float] = None,
    ):
        """
        Sets the discrete timesteps used for the diffusion chain (to be run before inference).

        Args:
            num_inference_steps (`int`):
                The number of diffusion steps used when generating samples with a pre-trained model.
            device (`str` or `torch.device`, *optional*):
                The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
        """

        if self.config.use_dynamic_shifting and mu is None:
            raise ValueError(
                " you have to pass a value for `mu` when `use_dynamic_shifting` is set to be `True`"
            )

        if sigmas is None:
            self.num_inference_steps = num_inference_steps
            timesteps = np.array(
                [
                    (1.0 - i / num_inference_steps) * self.config.num_train_timesteps
                    for i in range(num_inference_steps)
                ]
            )  # different from the original code in SD3
            sigmas = timesteps / self.config.num_train_timesteps

        if self.config.use_dynamic_shifting:
            sigmas = self.time_shift_dynamic(mu, 1.0, sigmas)
        else:
            sigmas = self.config.shift * sigmas / (1 + (self.config.shift - 1) * sigmas)

        sigmas = torch.from_numpy(sigmas).to(dtype=torch.float32, device=device)
        timesteps = sigmas * self.config.num_train_timesteps

        self.timesteps = timesteps.to(device=device)
        self.sigmas = torch.cat([sigmas, torch.zeros(1, device=sigmas.device)])

        self._step_index = None
        self._begin_index = None

    def index_for_timestep(self, timestep, schedule_timesteps=None):
        if schedule_timesteps is None:
            schedule_timesteps = self.timesteps

        indices = (schedule_timesteps == timestep).nonzero()

        # The sigma index that is taken for the **very** first `step`
        # is always the second index (or the last index if there is only 1)
        # This way we can ensure we don't accidentally skip a sigma in
        # case we start in the middle of the denoising schedule (e.g. for image-to-image)
        pos = 1 if len(indices) > 1 else 0

        return indices[pos].item()

    def _init_step_index(self, timestep):
        if self.begin_index is None:
            if isinstance(timestep, torch.Tensor):
                timestep = timestep.to(self.timesteps.device)
            self._step_index = self.index_for_timestep(timestep)
        else:
            self._step_index = self._begin_index

    def step(
        self,
        model_output: torch.FloatTensor,
        timestep: Union[float, torch.FloatTensor],
        sample: torch.FloatTensor,
        s_churn: float = 0.0,
        s_tmin: float = 0.0,
        s_tmax: float = float("inf"),
        s_noise: float = 1.0,
        generator: Optional[torch.Generator] = None,
        return_dict: bool = True,
    ) -> Union[RectifiedFlowSchedulerOutput, Tuple]:
        """
        Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
        process from the learned model outputs (most often the predicted noise).

        Args:
            model_output (`torch.FloatTensor`):
                The direct output from learned diffusion model.
            timestep (`float`):
                The current discrete timestep in the diffusion chain.
            sample (`torch.FloatTensor`):
                A current instance of a sample created by the diffusion process.
            s_churn (`float`):
            s_tmin  (`float`):
            s_tmax  (`float`):
            s_noise (`float`, defaults to 1.0):
                Scaling factor for noise added to the sample.
            generator (`torch.Generator`, *optional*):
                A random number generator.
            return_dict (`bool`):
                Whether or not to return a [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] or
                tuple.

        Returns:
            [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] or `tuple`:
                If return_dict is `True`, [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] is
                returned, otherwise a tuple is returned where the first element is the sample tensor.
        """

        if (
            isinstance(timestep, int)
            or isinstance(timestep, torch.IntTensor)
            or isinstance(timestep, torch.LongTensor)
        ):
            raise ValueError(
                (
                    "Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
                    " `EulerDiscreteScheduler.step()` is not supported. Make sure to pass"
                    " one of the `scheduler.timesteps` as a timestep."
                ),
            )

        if self.step_index is None:
            self._init_step_index(timestep)

        # Upcast to avoid precision issues when computing prev_sample
        sample = sample.to(torch.float32)

        sigma = self.sigmas[self.step_index]
        sigma_next = self.sigmas[self.step_index + 1]

        # Here different directions are used for the flow matching
        prev_sample = sample + (sigma - sigma_next) * model_output

        # Cast sample back to model compatible dtype
        prev_sample = prev_sample.to(model_output.dtype)

        # upon completion increase step index by one
        self._step_index += 1

        if not return_dict:
            return (prev_sample,)

        return RectifiedFlowSchedulerOutput(prev_sample=prev_sample)

    def scale_noise(
        self,
        original_samples: torch.Tensor,
        noise: torch.Tensor,
        timesteps: torch.IntTensor,
    ) -> torch.Tensor:
        """
        Forward function for the noise scaling in the flow matching.
        """
        sigmas = self._t_to_sigma(timesteps.to(dtype=torch.float32))

        while len(sigmas.shape) < len(original_samples.shape):
            sigmas = sigmas.unsqueeze(-1)

        return (1.0 - sigmas) * original_samples + sigmas * noise

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