  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.
