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.

翻译：我们提出了无模拟分数流匹配（[SF]²M）方法，这是一种无需模拟的目标函数，用于从任意源分布和目标分布提取的非配对样本中推断随机动力学。该方法统一了扩散模型训练中使用的分数匹配损失与近期连续归一化流训练中提出的流匹配损失。[SF]²M将连续时间随机生成建模诠释为薛定谔桥问题，通过静态熵正则化最优传输或小批量近似，在无需模拟学习随机过程的前提下高效学习薛定谔桥。实验表明，[SF]²M相比现有基于模拟的方法具有更高效率，且能获得更精确的薛定谔桥解。最后，我们将[SF]²M应用于快照数据中的细胞动力学学习问题。值得注意的是，[SF]²M首次实现了高维细胞动力学的精准建模，并能够从模拟数据中恢复已知的基因调控网络。我们的代码已开源至TorchCFM软件包：https://github.com/atong01/conditional-flow-matching。