Simulation-free Schrödinger bridges via score and flow matching
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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.
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