tts/modules/llm_dit/cfm.py

# MIT License

# Copyright (c) 2023 Alexander Tong

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# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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# SOFTWARE.

# Copyright (c) [2023] [Alexander Tong] 
# Copyright (c) [2025] [Ziyue Jiang] 
# SPDX-License-Identifier: MIT
# This file has been modified by Ziyue Jiang on 2025/03/19
# Original file was released under MIT, with the full license text # available at https://github.com/atong01/conditional-flow-matching/blob/1.0.7/LICENSE.
# This modified file is released under the same license.

import math
import torch
from typing import Union
from torch.distributions import LogisticNormal


class LogitNormalTrainingTimesteps:
    def __init__(self, T=1000.0, loc=0.0, scale=1.0):
        assert T > 0
        self.T = T
        self.dist = LogisticNormal(loc, scale)

    def sample(self, size, device):
        t = self.dist.sample(size)[..., 0].to(device)
        return t
    

def pad_t_like_x(t, x):
    """Function to reshape the time vector t by the number of dimensions of x.

    Parameters
    ----------
    x : Tensor, shape (bs, *dim)
        represents the source minibatch
    t : FloatTensor, shape (bs)

    Returns
    -------
    t : Tensor, shape (bs, number of x dimensions)

    Example
    -------
    x: Tensor (bs, C, W, H)
    t: Vector (bs)
    pad_t_like_x(t, x): Tensor (bs, 1, 1, 1)
    """
    if isinstance(t, (float, int)):
        return t
    return t.reshape(-1, *([1] * (x.dim() - 1)))


class ConditionalFlowMatcher:
    """Base class for conditional flow matching methods. This class implements the independent
    conditional flow matching methods from [1] and serves as a parent class for all other flow
    matching methods.

    It implements:
    - Drawing data from gaussian probability path N(t * x1 + (1 - t) * x0, sigma) function
    - conditional flow matching ut(x1|x0) = x1 - x0
    - score function $\nabla log p_t(x|x0, x1)$
    """

    def __init__(self, sigma: Union[float, int] = 0.0):
        r"""Initialize the ConditionalFlowMatcher class. It requires the hyper-parameter $\sigma$.

        Parameters
        ----------
        sigma : Union[float, int]
        """
        self.sigma = sigma
        self.time_sampler = LogitNormalTrainingTimesteps()

    def compute_mu_t(self, x0, x1, t):
        """
        Compute the mean of the probability path N(t * x1 + (1 - t) * x0, sigma), see (Eq.14) [1].

        Parameters
        ----------
        x0 : Tensor, shape (bs, *dim)
            represents the source minibatch
        x1 : Tensor, shape (bs, *dim)
            represents the target minibatch
        t : FloatTensor, shape (bs)

        Returns
        -------
        mean mu_t: t * x1 + (1 - t) * x0

        References
        ----------
        [1] Improving and Generalizing Flow-Based Generative Models with minibatch optimal transport, Preprint, Tong et al.
        """
        t = pad_t_like_x(t, x0)
        return t * x1 + (1 - t) * x0

    def compute_sigma_t(self, t):
        """
        Compute the standard deviation of the probability path N(t * x1 + (1 - t) * x0, sigma), see (Eq.14) [1].

        Parameters
        ----------
        t : FloatTensor, shape (bs)

        Returns
        -------
        standard deviation sigma

        References
        ----------
        [1] Improving and Generalizing Flow-Based Generative Models with minibatch optimal transport, Preprint, Tong et al.
        """
        del t
        return self.sigma

    def sample_xt(self, x0, x1, t, epsilon):
        """
        Draw a sample from the probability path N(t * x1 + (1 - t) * x0, sigma), see (Eq.14) [1].

        Parameters
        ----------
        x0 : Tensor, shape (bs, *dim)
            represents the source minibatch
        x1 : Tensor, shape (bs, *dim)
            represents the target minibatch
        t : FloatTensor, shape (bs)
        epsilon : Tensor, shape (bs, *dim)
            noise sample from N(0, 1)

        Returns
        -------
        xt : Tensor, shape (bs, *dim)

        References
        ----------
        [1] Improving and Generalizing Flow-Based Generative Models with minibatch optimal transport, Preprint, Tong et al.
        """
        mu_t = self.compute_mu_t(x0, x1, t)
        sigma_t = self.compute_sigma_t(t)
        sigma_t = pad_t_like_x(sigma_t, x0)
        return mu_t + sigma_t * epsilon

    def compute_conditional_flow(self, x0, x1, t, xt):
        """
        Compute the conditional vector field ut(x1|x0) = x1 - x0, see Eq.(15) [1].

        Parameters
        ----------
        x0 : Tensor, shape (bs, *dim)
            represents the source minibatch
        x1 : Tensor, shape (bs, *dim)
            represents the target minibatch
        t : FloatTensor, shape (bs)
        xt : Tensor, shape (bs, *dim)
            represents the samples drawn from probability path pt

        Returns
        -------
        ut : conditional vector field ut(x1|x0) = x1 - x0

        References
        ----------
        [1] Improving and Generalizing Flow-Based Generative Models with minibatch optimal transport, Preprint, Tong et al.
        """
        del t, xt
        return x1 - x0

    def sample_noise_like(self, x):
        return torch.randn_like(x)

    def sample_location_and_conditional_flow(self, x0, x1, t=None, return_noise=False):
        """
        Compute the sample xt (drawn from N(t * x1 + (1 - t) * x0, sigma))
        and the conditional vector field ut(x1|x0) = x1 - x0, see Eq.(15) [1].

        Parameters
        ----------
        x0 : Tensor, shape (bs, *dim)
            represents the source minibatch
        x1 : Tensor, shape (bs, *dim)
            represents the target minibatch
        (optionally) t : Tensor, shape (bs)
            represents the time levels
            if None, drawn from uniform [0,1]
        return_noise : bool
            return the noise sample epsilon


        Returns
        -------
        t : FloatTensor, shape (bs)
        xt : Tensor, shape (bs, *dim)
            represents the samples drawn from probability path pt
        ut : conditional vector field ut(x1|x0) = x1 - x0
        (optionally) eps: Tensor, shape (bs, *dim) such that xt = mu_t + sigma_t * epsilon

        References
        ----------
        [1] Improving and Generalizing Flow-Based Generative Models with minibatch optimal transport, Preprint, Tong et al.
        """
        if t is None:
            # t = torch.rand(x0.shape[0]).type_as(x0)
            t = self.time_sampler.sample([x0.shape[0]], x0.device).type_as(x0)

        assert len(t) == x0.shape[0], "t has to have batch size dimension"

        eps = self.sample_noise_like(x0)
        xt = self.sample_xt(x0, x1, t, eps)
        ut = self.compute_conditional_flow(x0, x1, t, xt)
        if return_noise:
            return t, xt, ut, eps
        else:
            return t, xt, ut

    def compute_lambda(self, t):
        """Compute the lambda function, see Eq.(23) [3].

        Parameters
        ----------
        t : FloatTensor, shape (bs)

        Returns
        -------
        lambda : score weighting function

        References
        ----------
        [4] Simulation-free Schrodinger bridges via score and flow matching, Preprint, Tong et al.
        """
        sigma_t = self.compute_sigma_t(t)
        return 2 * sigma_t / (self.sigma**2 + 1e-8)


class VariancePreservingConditionalFlowMatcher(ConditionalFlowMatcher):
    """Albergo et al. 2023 trigonometric interpolants class. This class inherits the
    ConditionalFlowMatcher and override the compute_mu_t and compute_conditional_flow functions in
    order to compute [3]'s trigonometric interpolants.

    [3] Stochastic Interpolants: A Unifying Framework for Flows and Diffusions, Albergo et al.
    """

    def compute_mu_t(self, x0, x1, t):
        r"""Compute the mean of the probability path (Eq.5) from [3].

        Parameters
        ----------
        x0 : Tensor, shape (bs, *dim)
            represents the source minibatch
        x1 : Tensor, shape (bs, *dim)
            represents the target minibatch
        t : FloatTensor, shape (bs)

        Returns
        -------
        mean mu_t: cos(pi t/2)x0 + sin(pi t/2)x1

        References
        ----------
        [3] Stochastic Interpolants: A Unifying Framework for Flows and Diffusions, Albergo et al.
        """
        t = pad_t_like_x(t, x0)
        return torch.cos(math.pi / 2 * t) * x0 + torch.sin(math.pi / 2 * t) * x1

    def compute_conditional_flow(self, x0, x1, t, xt):
        r"""Compute the conditional vector field similar to [3].

        ut(x1|x0) = pi/2 (cos(pi*t/2) x1 - sin(pi*t/2) x0),
        see Eq.(21) [3].

        Parameters
        ----------
        x0 : Tensor, shape (bs, *dim)
            represents the source minibatch
        x1 : Tensor, shape (bs, *dim)
            represents the target minibatch
        t : FloatTensor, shape (bs)
        xt : Tensor, shape (bs, *dim)
            represents the samples drawn from probability path pt

        Returns
        -------
        ut : conditional vector field
        ut(x1|x0) = pi/2 (cos(pi*t/2) x1 - sin(\pi*t/2) x0)

        References
        ----------
        [3] Stochastic Interpolants: A Unifying Framework for Flows and Diffusions, Albergo et al.
        """
        del xt
        t = pad_t_like_x(t, x0)
        return math.pi / 2 * (torch.cos(math.pi / 2 * t) * x1 - torch.sin(math.pi / 2 * t) * x0)