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

• URL: http://arxiv.org/abs/2307.03672v3
• Date: Mon, 11 Mar 2024 14:42:58 GMT
• Title: Simulation-free Schr\"odinger bridges via score and flow matching
• Authors: Alexander Tong, Nikolay Malkin, Kilian Fatras, Lazar Atanackovic, Yanlei Zhang, Guillaume Huguet, Guy Wolf, Yoshua Bengio
• Abstract summary: We present simulation-free score and flow matching ([SF]$2$M) 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 flows. Notably, [SF]$2$M is the first method to accurately model cell dynamics in high dimensions and can recover known gene regulatory networks simulated data.
• Score: 89.4231207928885
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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