2023/07/07 by Alexander Tong, Tong, Alexander, Nikolay Malkin +13 · 26 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Code (set theory) #Computer science #Cross entropy #Entropy (arrow of time) #FOS: Computer and information sciences #Flow (mathematics) #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Generative grammar #Machine Learning (cs.LG) #Matching (statistics) #Mathematical optimization #Mathematics #Model Reduction and Neural Networks #Principle of maximum entropy #Snapshot (computer storage) #Source code #Statistics #Theoretical computer science
paper · pdf · doi:10.48550/arxiv.2307.03672
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We present simulation-free score and flow matching ([SF]2M), 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]2M 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]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. Our code is available in the TorchCFM package at https://github.com/atong01/conditional-flow-matching.