Action Matching: Learning Stochastic Dynamics from Samples

TL;DR

Action Matching is a novel method for learning stochastic dynamics from uncorrelated samples, enabling trajectory simulation without relying on explicit assumptions or complex solvers, with applications across sciences and generative modeling.

Contribution

It introduces a new training objective for learning dynamics from independent samples, extending to stochastic and mass-changing systems, without requiring backpropagation through differential equations.

Findings

Achieves competitive results in biological, physical, and generative modeling tasks.

Effectively learns stochastic differential equations and systems with creation/destruction of probability mass.

Provides a scalable, assumption-free approach to modeling continuous dynamics from snapshot data.

Abstract

Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative modeling. In these settings, we assume access to cross-sectional samples that are uncorrelated over time, rather than full trajectories of samples. In order to better understand the systems under observation, we would like to learn a model of the underlying process that allows us to propagate samples in time and thereby simulate entire individual trajectories. In this work, we propose Action Matching, a method for learning a rich family of dynamics using only independent samples from its time evolution. We derive a tractable training objective, which does not rely on explicit assumptions about the underlying dynamics and does not require back-propagation through differential equations or optimal transport solvers. Inspired by connections with optimal transport, we derive extensions of Action Matching to learn stochastic differential equations and dynamics involving creation and destruction of probability mass. Finally, we showcase applications of Action Matching by achieving competitive performance in a diverse set of experiments from biology, physics, and generative modeling.