Latent Process Generator Matching

2026-05-19

AI Summary

This work addresses the lack of a general framework for modeling time-varying latent states in existing generative models, which often rely on auxiliary stochastic processes that are difficult to sample. The authors propose a novel approach that treats observation generation as a deterministic mapping of a tractable Markov process, employing an image-space stochastic process generator whose one-time marginal distribution matches that of a target projected process. The key innovation lies in extending Generator Matching—previously limited to static latent variables—to time-varying latent processes for the first time. By integrating stochastic process theory, Markov projections, and flow matching techniques, the method establishes a unified generative modeling framework. This framework not only subsumes existing models with discrete latent processes as special cases but also accommodates a broader class of time-varying latent conditions while rigorously ensuring consistency between the generated and target marginal distributions.

Abstract

Many recent flow-matching and diffusion-style generative models rely on auxiliary stochastic dynamics during training: a richer process is simulated to define conditional targets, but the auxiliary state is either intractable to sample at generation time or simply not part of the desired output. Existing Generator Matching theory formalises conditioning on static latent random variables, and several recent papers prove special cases of projection results for particular augmented-state constructions. We introduce latent process generator matching, a general framework that treats the observed generative state as a deterministic image $X_t=Φ(Y_t)$ of a tractable Markov process $Y_t$. We show that in this setting one may learn the generator of a stochastic process on the image space which has the same one-time marginal distributions as the projected process. This generalizes and subsumes the discrete latent process results from the literature, and extends Generator Matching from static latent variables to a rich family of time-dependent latent conditional processes.

Problem

• latent process
• generator matching
• stochastic dynamics
• conditional processes
• generative models

Innovation

• latent process
• generator matching
• stochastic dynamics
• Markov process
• flow matching