FlowMatching#

class deepinv.sampling.FlowMatching(a_t=lambda t: ..., a_prime_t=lambda t: ..., b_t=lambda t: ..., b_prime_t=lambda t: ..., T=0.99, alpha=0.0, denoiser=None, solver=None, dtype=torch.float64, device=torch.device('cpu'), *args, **kwargs)[source]#

Bases: EDMDiffusionSDE

Generative Flow Matching process.

It corresponds to the reverse-time SDE of the following forward-time noising process, which corresponds to a linear interpolation between data and Gaussian noise:

\[x_t = a_t x_0 + b_t z \quad \mbox{ where } x_0 \sim p_{data} \mbox{ and } z \sim \mathcal{N}(0, I)\]

The schedulers \(a(t)\) and \(b(t)\) must satisfy \(a(0) = 1\), \(b(0) = 0\), \(a(1) = 0\), and \(b(1) = 1\).

Compared to the EDM formulation in deepinv.sampling.EDMDiffusionSDE, the scale \(s(t)\) and noise \(\sigma(t)\) schedulers are defined with respect to \(a(t)\) and \(b(t)\) as follows:

\[s(t) = a(t), \quad \sigma(t) = \frac{b(t)}{a(t)} .\]

Note

This SDE must be solved going reverse in time i.e. from \(t=1\) to \(t=0\). Note that in order to unify flow matching and diffusion models, we set the starting time of the generating process (noise distribution) to be 1, and the ending time of the generating process (data distribution) to be 0, which is different from the convention in the flow matching literature.

Parameters:

  • a_t (Callable) – time-dependent parameter \(a(t)\) of flow-matching. Default to lambda t: 1-t.

  • a_prime_t (Callable) – time derivative \(a'(t)\) of \(a(t)\). Default to lambda t: -1.

  • b_t (Callable) – time-dependent parameter \(b(t)\) of flow-matching.Default to lambda t: t.

  • b_prime_t (Callable) – time derivative \(b'(t)\) of \(b(t)\). Default to lambda t: 1.

  • denoiser (deepinv.models.Denoiser) – a denoiser used to provide an approximation of the score at time \(t\): \(\nabla \log p_t\).

  • alpha (Callable, float) – a (possibly time-dependent) positive scalar weighting the diffusion term. A constant function \(\alpha(t) = 0\) corresponds to ODE sampling and \(\alpha(t) > 0\) corresponds to SDE sampling.

  • solver (deepinv.sampling.BaseSDESolver) – the solver for solving the SDE.

  • dtype (torch.dtype) – data type of the computation, except for the denoiser which will use torch.float32. We recommend using torch.float64 for better stability and less numerical error when solving the SDE in discrete time, since most computation cost is from evaluating the denoiser, which will be always computed in torch.float32.

  • device (torch.device) – device on which the computation is performed.

  • *args – additional arguments for the deepinv.sampling.DiffusionSDE.

  • **kwargs – additional keyword arguments for the deepinv.sampling.DiffusionSDE.

velocity(x, t, *args, **kwargs)[source]#

Computes the velocity field of the flow matching process, which is defined as the drift of the backward SDE.

Parameters:

  • x (torch.Tensor) – current state

  • t (torch.Tensor, float) – current timestep

  • *args – additional arguments for the denoiser.

  • **kwargs – additional keyword arguments for the denoiser, e.g., class_labels for class-conditional models.

Returns:

the velocity field at state x and time t.

Return type:

torch.Tensor

Examples using FlowMatching:#

Flow-Matching for posterior sampling and unconditional generation

Flow-Matching for posterior sampling and unconditional generation