Stream-level flow matching from a Bayesian decision theoretic perspective

Music City Center 

Flow matching is a family of training algorithms for fitting continuous normalizing flows (CNFs). A standard approach to FM, called conditional flow matching (CFM), exploits the fact that the marginal vector field of a CNF can be trained by least-square regression on the conditional vector field given one or both ends of the flow path. We show that viewing CFM training from a Bayesian decision theoretic perspective on parameter estimation opens the door to generalizations of CFM. We present one such extension by defining conditional probability paths given what we call "streams", or instances of latent stochastic paths that connect pairs of noise and observed data. We advocate the modeling of these latent streams using Gaussian processes (GPs), whose distributional properties allow sampling from the resulting conditional probability paths without simulating the streams. This GP-based stream-level CFM can substantially reduce the variance in the estimated marginal vector field at a moderate computational cost, thereby improving the generated samples under common metrics. It also allows for flexibly linking multiple related training data points and incorporating prior information.

generative models

normalizing flows

nonparametric methods

latent variable models

hierarchical models