Simulation-free Schr\"odinger bridges via score and flow matching

TL;DR

This paper introduces SF2M, a simulation-free method for learning stochastic dynamics and Schr"odinger bridges from unpaired data, improving efficiency and accuracy over previous simulation-based approaches, with applications in cell dynamics modeling.

Contribution

SF2M generalizes score and flow matching for Schr"odinger bridge problems, enabling efficient, simulation-free learning of stochastic processes from unpaired data.

Findings

SF2M outperforms simulation-based methods in accuracy and efficiency.

SF2M successfully models high-dimensional cell dynamics.

SF2M recovers gene regulatory networks from simulated data.

Abstract

We present simulation-free score and flow matching ([SF]$^2$M), a simulation-free objective for inferring stochastic dynamics given unpaired samples drawn from arbitrary source and target 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 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. Our code is available in the TorchCFM package at https://github.com/atong01/conditional-flow-matching.