Simulation-Free Schrodinger Bridges via Score and Flow Matching

Abstract

We present simulation-free score and flow matching ([SF]2M), a simulation-free objective for inferring stochastic dynamics given unpaired source and target samples drawn from arbitrary distributions. Our method generalizes both the score-matching loss used in the training of diffusion models and the recently proposed flow matching loss used in the training of continuous normalizing flows. [SF]2M interprets continuous-time stochastic generative modeling as a Schrödinger bridge (SB) problem. It relies on static entropy-regularized optimal transport, or a minibatch approximation, to efficiently learn the SB without simulating the learned stochastic process. We find that [SF]2M is more efficient and gives more accurate solutions to the SB problem than simulation-based methods from prior work. Finally, we apply [SF]2M to the problem of learning cell dynamics from snapshot data. Notably, [SF]2M is the first method to accurately model cell dynamics in high dimensions and can recover known gene regulatory networks from simulated data.

Alex Tong

Postdoctoral Fellow

My research interests include optimal transport, graph scattering, and normalizing flows.