Simulation-Free Schrödinger Bridges via Score and Flow Matching

Alexander Tong, Nikolay Malkin, Kilian FATRAS, Lazar Atanackovic, Yanlei Zhang, Guillaume Huguet, Guy Wolf, Yoshua Bengio

Keywords: SDE, diffusion, single-cell, optimal transport

TL;DR: Generalization of conditional flow matching to SDEs enabling simulation-free Schrödinger bridge fitting, with applications to cell dynamics.

Abstract: We present simulation-free score and flow matching ([SF]$^2$M), 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]$^2$M interprets continuous-time stochastic generative modeling as a Schr\"odinger 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]$^2$M is more efficient and gives more accurate solutions to the SB problem than simulation-based methods from prior work. Finally, we apply [SF]$^2$M to the problem of learning cell dynamics from snapshot data. Notably, [SF]$^2$M is the first method to accurately model cell dynamics in high dimensions and can recover known gene regulatory networks from simulated data.

Submission Number: 76