FlowMatchEulerDiscreteScheduler.py

# Copyright 2025 Stability AI, Katherine Crowson 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.

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

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, is_scipy_available, logging
from .scheduling_utils import SchedulerMixin
from pytorch_wavelets import DWTForward, DWTInverse

if is_scipy_available():
    import scipy.stats

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


@dataclass
class FlowMatchEulerDiscreteSchedulerOutput(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 FlowMatchEulerDiscreteScheduler(SchedulerMixin, ConfigMixin):
    """
    Euler scheduler.

    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.
        shift (`float`, defaults to 1.0):
            The shift value for the timestep schedule.
        use_dynamic_shifting (`bool`, defaults to False):
            Whether to apply timestep shifting on-the-fly based on the image resolution.
        base_shift (`float`, defaults to 0.5):
            Value to stabilize image generation. Increasing `base_shift` reduces variation and image is more consistent
            with desired output.
        max_shift (`float`, defaults to 1.15):
            Value change allowed to latent vectors. Increasing `max_shift` encourages more variation and image may be
            more exaggerated or stylized.
        base_image_seq_len (`int`, defaults to 256):
            The base image sequence length.
        max_image_seq_len (`int`, defaults to 4096):
            The maximum image sequence length.
        invert_sigmas (`bool`, defaults to False):
            Whether to invert the sigmas.
        shift_terminal (`float`, defaults to None):
            The end value of the shifted timestep schedule.
        use_karras_sigmas (`bool`, defaults to False):
            Whether to use Karras sigmas for step sizes in the noise schedule during sampling.
        use_exponential_sigmas (`bool`, defaults to False):
            Whether to use exponential sigmas for step sizes in the noise schedule during sampling.
        use_beta_sigmas (`bool`, defaults to False):
            Whether to use beta sigmas for step sizes in the noise schedule during sampling.
        time_shift_type (`str`, defaults to "exponential"):
            The type of dynamic resolution-dependent timestep shifting to apply. Either "exponential" or "linear".
        stochastic_sampling (`bool`, defaults to False):
            Whether to use stochastic sampling.
    """

    _compatibles = []
    order = 1

    @register_to_config
    def __init__(
        self,
        num_train_timesteps: int = 1000,
        shift: float = 1.0,
        use_dynamic_shifting: bool = False,
        base_shift: Optional[float] = 0.5,
        max_shift: Optional[float] = 1.15,
        base_image_seq_len: Optional[int] = 256,
        max_image_seq_len: Optional[int] = 4096,
        invert_sigmas: bool = False,
        shift_terminal: Optional[float] = None,
        use_karras_sigmas: Optional[bool] = False,
        use_exponential_sigmas: Optional[bool] = False,
        use_beta_sigmas: Optional[bool] = False,
        time_shift_type: str = "exponential",
        stochastic_sampling: bool = False,
    ):
        if self.config.use_beta_sigmas and not is_scipy_available():
            raise ImportError("Make sure to install scipy if you want to use beta sigmas.")
        if sum([self.config.use_beta_sigmas, self.config.use_exponential_sigmas, self.config.use_karras_sigmas]) > 1:
            raise ValueError(
                "Only one of `config.use_beta_sigmas`, `config.use_exponential_sigmas`, `config.use_karras_sigmas` can be used."
            )
        if time_shift_type not in {"exponential", "linear"}:
            raise ValueError("`time_shift_type` must either be 'exponential' or 'linear'.")

        timesteps = np.linspace(1, num_train_timesteps, num_train_timesteps, dtype=np.float32)[::-1].copy()
        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 = shift * sigmas / (1 + (shift - 1) * sigmas)

        self.timesteps = sigmas * num_train_timesteps

        self._step_index = None
        self._begin_index = None

        self._shift = shift

        self.sigmas = sigmas.to("cpu")  # to avoid too much CPU/GPU communication
        self.sigma_min = self.sigmas[-1].item()
        self.sigma_max = self.sigmas[0].item()
        # define dwt and iwt
        self.dwt = DWTForward(J=1, mode='zero', wave='haar').cuda() # haar db4 sym8
        self.iwt = DWTInverse(mode='zero', wave='haar').cuda() 

    @property
    def shift(self):
        """
        The value used for shifting.
        """
        return self._shift

    @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 set_shift(self, shift: float):
        self._shift = shift

    def scale_noise(
        self,
        sample: torch.FloatTensor,
        timestep: Union[float, torch.FloatTensor],
        noise: Optional[torch.FloatTensor] = None,
    ) -> torch.FloatTensor:
        """
        Forward process in flow-matching

        Args:
            sample (`torch.FloatTensor`):
                The input sample.
            timestep (`int`, *optional*):
                The current timestep in the diffusion chain.

        Returns:
            `torch.FloatTensor`:
                A scaled input sample.
        """
        # Make sure sigmas and timesteps have the same device and dtype as original_samples
        sigmas = self.sigmas.to(device=sample.device, dtype=sample.dtype)

        if sample.device.type == "mps" and torch.is_floating_point(timestep):
            # mps does not support float64
            schedule_timesteps = self.timesteps.to(sample.device, dtype=torch.float32)
            timestep = timestep.to(sample.device, dtype=torch.float32)
        else:
            schedule_timesteps = self.timesteps.to(sample.device)
            timestep = timestep.to(sample.device)

        # self.begin_index is None when scheduler is used for training, or pipeline does not implement set_begin_index
        if self.begin_index is None:
            step_indices = [self.index_for_timestep(t, schedule_timesteps) for t in timestep]
        elif self.step_index is not None:
            # add_noise is called after first denoising step (for inpainting)
            step_indices = [self.step_index] * timestep.shape[0]
        else:
            # add noise is called before first denoising step to create initial latent(img2img)
            step_indices = [self.begin_index] * timestep.shape[0]

        sigma = sigmas[step_indices].flatten()
        while len(sigma.shape) < len(sample.shape):
            sigma = sigma.unsqueeze(-1)

        sample = sigma * noise + (1.0 - sigma) * sample

        return sample

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

    def time_shift(self, mu: float, sigma: float, t: torch.Tensor):
        if self.config.time_shift_type == "exponential":
            return self._time_shift_exponential(mu, sigma, t)
        elif self.config.time_shift_type == "linear":
            return self._time_shift_linear(mu, sigma, t)

    def stretch_shift_to_terminal(self, t: torch.Tensor) -> torch.Tensor:
        r"""
        Stretches and shifts the timestep schedule to ensure it terminates at the configured `shift_terminal` config
        value.

        Reference:
        https://github.com/Lightricks/LTX-Video/blob/a01a171f8fe3d99dce2728d60a73fecf4d4238ae/ltx_video/schedulers/rf.py#L51

        Args:
            t (`torch.Tensor`):
                A tensor of timesteps to be stretched and shifted.

        Returns:
            `torch.Tensor`:
                A tensor of adjusted timesteps such that the final value equals `self.config.shift_terminal`.
        """
        one_minus_z = 1 - t
        scale_factor = one_minus_z[-1] / (1 - self.config.shift_terminal)
        stretched_t = 1 - (one_minus_z / scale_factor)
        return stretched_t

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

        Args:
            num_inference_steps (`int`, *optional*):
                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.
            sigmas (`List[float]`, *optional*):
                Custom values for sigmas to be used for each diffusion step. If `None`, the sigmas are computed
                automatically.
            mu (`float`, *optional*):
                Determines the amount of shifting applied to sigmas when performing resolution-dependent timestep
                shifting.
            timesteps (`List[float]`, *optional*):
                Custom values for timesteps to be used for each diffusion step. If `None`, the timesteps are computed
                automatically.
        """
        if self.config.use_dynamic_shifting and mu is None:
            raise ValueError("`mu` must be passed when `use_dynamic_shifting` is set to be `True`")

        if sigmas is not None and timesteps is not None:
            if len(sigmas) != len(timesteps):
                raise ValueError("`sigmas` and `timesteps` should have the same length")

        if num_inference_steps is not None:
            if (sigmas is not None and len(sigmas) != num_inference_steps) or (
                timesteps is not None and len(timesteps) != num_inference_steps
            ):
                raise ValueError(
                    "`sigmas` and `timesteps` should have the same length as num_inference_steps, if `num_inference_steps` is provided"
                )
        else:
            num_inference_steps = len(sigmas) if sigmas is not None else len(timesteps)

        self.num_inference_steps = num_inference_steps

        # 1. Prepare default sigmas
        is_timesteps_provided = timesteps is not None

        if is_timesteps_provided:
            timesteps = np.array(timesteps).astype(np.float32)

        if sigmas is None:
            if timesteps is None:
                timesteps = np.linspace(
                    self._sigma_to_t(self.sigma_max), self._sigma_to_t(self.sigma_min), num_inference_steps
                )
            sigmas = timesteps / self.config.num_train_timesteps
        else:
            sigmas = np.array(sigmas).astype(np.float32)
            num_inference_steps = len(sigmas)

        # 2. Perform timestep shifting. Either no shifting is applied, or resolution-dependent shifting of
        #    "exponential" or "linear" type is applied
        if self.config.use_dynamic_shifting:
            sigmas = self.time_shift(mu, 1.0, sigmas)
        else:
            sigmas = self.shift * sigmas / (1 + (self.shift - 1) * sigmas)

        # 3. If required, stretch the sigmas schedule to terminate at the configured `shift_terminal` value
        if self.config.shift_terminal:
            sigmas = self.stretch_shift_to_terminal(sigmas)

        # 4. If required, convert sigmas to one of karras, exponential, or beta sigma schedules
        if self.config.use_karras_sigmas:
            sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
        elif self.config.use_exponential_sigmas:
            sigmas = self._convert_to_exponential(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
        elif self.config.use_beta_sigmas:
            sigmas = self._convert_to_beta(in_sigmas=sigmas, num_inference_steps=num_inference_steps)

        # 5. Convert sigmas and timesteps to tensors and move to specified device
        sigmas = torch.from_numpy(sigmas).to(dtype=torch.float32, device=device)
        if not is_timesteps_provided:
            timesteps = sigmas * self.config.num_train_timesteps
        else:
            timesteps = torch.from_numpy(timesteps).to(dtype=torch.float32, device=device)

        # 6. Append the terminal sigma value.
        #    If a model requires inverted sigma schedule for denoising but timesteps without inversion, the
        #    `invert_sigmas` flag can be set to `True`. This case is only required in Mochi
        if self.config.invert_sigmas:
            sigmas = 1.0 - sigmas
            timesteps = sigmas * self.config.num_train_timesteps
            sigmas = torch.cat([sigmas, torch.ones(1, device=sigmas.device)])
        else:
            sigmas = torch.cat([sigmas, torch.zeros(1, device=sigmas.device)])

        self.timesteps = timesteps
        self.sigmas = sigmas
        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,
        scaler: float = 0.0,
        generator: Optional[torch.Generator] = None,
        per_token_timesteps: Optional[torch.Tensor] = None,
        return_dict: bool = True,
    ) -> Union[FlowMatchEulerDiscreteSchedulerOutput, 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.
            per_token_timesteps (`torch.Tensor`, *optional*):
                The timesteps for each token in the sample.
            return_dict (`bool`):
                Whether or not to return a
                [`~schedulers.scheduling_flow_match_euler_discrete.FlowMatchEulerDiscreteSchedulerOutput`] or tuple.

        Returns:
            [`~schedulers.scheduling_flow_match_euler_discrete.FlowMatchEulerDiscreteSchedulerOutput`] or `tuple`:
                If return_dict is `True`,
                [`~schedulers.scheduling_flow_match_euler_discrete.FlowMatchEulerDiscreteSchedulerOutput`] 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"
                    " `FlowMatchEulerDiscreteScheduler.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)

        if per_token_timesteps is not None:
            per_token_sigmas = per_token_timesteps / self.config.num_train_timesteps

            sigmas = self.sigmas[:, None, None]
            lower_mask = sigmas < per_token_sigmas[None] - 1e-6
            lower_sigmas = lower_mask * sigmas
            lower_sigmas, _ = lower_sigmas.max(dim=0)

            current_sigma = per_token_sigmas[..., None]
            next_sigma = lower_sigmas[..., None]
            dt = current_sigma - next_sigma
        else:
            sigma_idx = self.step_index
            sigma = self.sigmas[sigma_idx]
            sigma_next = self.sigmas[sigma_idx + 1]

            current_sigma = sigma
            next_sigma = sigma_next
            dt = sigma_next - sigma

        if self.config.stochastic_sampling:
            x0 = sample - current_sigma * model_output
            noise = torch.randn_like(sample)
            prev_sample = (1.0 - next_sigma) * x0 + next_sigma * noise
        else:
            # scaler is the weight coefficient introduced by us, shown in Eqs.17, 20, and 21. And we recommend passing it in using the monkey patch approach.
            x0 = sample - current_sigma * model_output 
            prev_sample = sample + dt * model_output
            prev_sample = prev_sample + scaler * (prev_sample - x0) # Differential Correction in Pixel Space - Eq.17
            # prev_sample = prev_sample + scaler * (sample - x0) # This form of correction in Pixel Space is also viable

            # prev_sample = self.dcw_low(prev_sample, x0, scaler) # Differential Correction in Wavelet Domain - Only low-frequency
            # prev_sample = self.dcw_high(prev_sample, x0, scaler) # Differential Correction in Wavelet Domain - Only high-frequency


        # upon completion increase step index by one
        self._step_index += 1
        if per_token_timesteps is None:
            # Cast sample back to model compatible dtype
            prev_sample = prev_sample.to(model_output.dtype)
        if not return_dict:
            return (prev_sample,)

        return FlowMatchEulerDiscreteSchedulerOutput(prev_sample=prev_sample)

    def dcw_low(self, x, y, scaler):
        orig_x_dim = x.dim()
        orig_y_dim = y.dim()
        x = x.to(torch.float32)
        y = y.to(torch.float32)
        # 4D [B, C, H, W]
        if x.dim() == 3:
            x = x.unsqueeze(0)  # [C, H, W] -> [1, C, H, W]
        elif x.dim() == 2:
            x = x.unsqueeze(0).unsqueeze(0)  # [H, W] -> [1, 1, H, W]
        if y.dim() == 3:
            y = y.unsqueeze(0)
        elif y.dim() == 2:
            y = y.unsqueeze(0).unsqueeze(0)
        if x.dim() != 4 or y.dim() != 4:
            raise ValueError(f"Unsupported input dims: x={orig_x_dim}, y={orig_y_dim}")
        xl, xh = self.dwt(x)
        yl, yh = self.dwt(y)
        xl = xl + scaler * (xl - yl)
        x_new = self.iwt((xl, xh))  # shape: [B, C, H, W]
        if orig_x_dim == 2:
            x_new = x_new.squeeze(0).squeeze(0)  # [1, 1, H, W] -> [H, W]
        elif orig_x_dim == 3:
            x_new = x_new.squeeze(0)  # [1, C, H, W] -> [C, H, W]
        return x_new
    
    def dcw_high(self, x, y, scaler):
        orig_x_dim = x.dim()
        orig_y_dim = y.dim()
        x = x.to(torch.float32)
        y = y.to(torch.float32)
        # 4D [B, C, H, W]
        if x.dim() == 3:
            x = x.unsqueeze(0)  # [C, H, W] -> [1, C, H, W]
        elif x.dim() == 2:
            x = x.unsqueeze(0).unsqueeze(0)  # [H, W] -> [1, 1, H, W]
        if y.dim() == 3:
            y = y.unsqueeze(0)
        elif y.dim() == 2:
            y = y.unsqueeze(0).unsqueeze(0)
        if x.dim() != 4 or y.dim() != 4:
            raise ValueError(f"Unsupported input dims: x={orig_x_dim}, y={orig_y_dim}")
        xl, xh = self.dwt(x)
        yl, yh = self.dwt(y)
        out = []
        for xh_band, yh_band in zip(xh, yh):
            out.append(xh_band + scaler * (xh_band - yh_band))
        xh = out
        x_new = self.iwt((xl, xh))  # shape: [B, C, H, W]
        if orig_x_dim == 2:
            x_new = x_new.squeeze(0).squeeze(0)  # [1, 1, H, W] -> [H, W]
        elif orig_x_dim == 3:
            x_new = x_new.squeeze(0)  # [1, C, H, W] -> [C, H, W]
        return x_new
    
    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
    def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
        """Constructs the noise schedule of Karras et al. (2022)."""

        # Hack to make sure that other schedulers which copy this function don't break
        # TODO: Add this logic to the other schedulers
        if hasattr(self.config, "sigma_min"):
            sigma_min = self.config.sigma_min
        else:
            sigma_min = None

        if hasattr(self.config, "sigma_max"):
            sigma_max = self.config.sigma_max
        else:
            sigma_max = None

        sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
        sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()

        rho = 7.0  # 7.0 is the value used in the paper
        ramp = np.linspace(0, 1, num_inference_steps)
        min_inv_rho = sigma_min ** (1 / rho)
        max_inv_rho = sigma_max ** (1 / rho)
        sigmas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
        return sigmas

    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
    def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
        """Constructs an exponential noise schedule."""

        # Hack to make sure that other schedulers which copy this function don't break
        # TODO: Add this logic to the other schedulers
        if hasattr(self.config, "sigma_min"):
            sigma_min = self.config.sigma_min
        else:
            sigma_min = None

        if hasattr(self.config, "sigma_max"):
            sigma_max = self.config.sigma_max
        else:
            sigma_max = None

        sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
        sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()

        sigmas = np.exp(np.linspace(math.log(sigma_max), math.log(sigma_min), num_inference_steps))
        return sigmas

    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_beta
    def _convert_to_beta(
        self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
    ) -> torch.Tensor:
        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""

        # Hack to make sure that other schedulers which copy this function don't break
        # TODO: Add this logic to the other schedulers
        if hasattr(self.config, "sigma_min"):
            sigma_min = self.config.sigma_min
        else:
            sigma_min = None

        if hasattr(self.config, "sigma_max"):
            sigma_max = self.config.sigma_max
        else:
            sigma_max = None

        sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
        sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()

        sigmas = np.array(
            [
                sigma_min + (ppf * (sigma_max - sigma_min))
                for ppf in [
                    scipy.stats.beta.ppf(timestep, alpha, beta)
                    for timestep in 1 - np.linspace(0, 1, num_inference_steps)
                ]
            ]
        )
        return sigmas

    def _time_shift_exponential(self, mu, sigma, t):
        return math.exp(mu) / (math.exp(mu) + (1 / t - 1) ** sigma)

    def _time_shift_linear(self, mu, sigma, t):
        return mu / (mu + (1 / t - 1) ** sigma)

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