Simulation-free Schrödinger bridges via score and flow matching
This work addresses the challenge of learning stochastic dynamics from snapshot data, particularly in high-dimensional domains like biology, offering a novel simulation-free approach that improves efficiency and accuracy.
The paper tackles the problem of inferring stochastic dynamics from unpaired samples by proposing simulation-free score and flow matching ([SF]^2M), which generalizes existing methods and interprets generative modeling as a Schrödinger bridge problem, resulting in more efficient and accurate solutions than prior simulation-based methods, with applications in high-dimensional cell dynamics modeling.
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 Schrödinger 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.