Action Matching: A Variational Method for Learning Stochastic Dynamics from Samples

Stochastic dynamics are ubiquitous in many fields of science, from the evolution of quantum systems in physics to diffusion-based models in machine learning. Existing methods such as score matching can be used to simulate these physical processes by assuming that the dynamics is a diffusion, which is not always the case. In this work, we propose a method called "Action Matching" that enables us to learn a much broader family of stochastic dynamics. Our method requires access only to samples from different time-steps, makes no explicit assumptions about the underlying dynamics, and can be applied even when samples are uncorrelated (i.e., are not part of a trajectory). Action Matching directly learns an underlying mechanism to move samples in time without modeling the distributions at each time-step. In this work, we showcase how Action Matching can be used for several computer vision tasks such as generative modeling, super-resolution, colorization, and inpainting; and further discuss potential applications in other areas of science.