We present simulation-free score and flow matching ([SF]$^2$M), 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]$^2$M interprets continuous-time stochastic generative modeling as a Schr\"odinger 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]$^2$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.

翻译：我们提出一种无需模拟的分数与流匹配方法（[SF]²M），这是一种在给定来自任意分布的非配对源样本和目标样本条件下，推断随机动力学的无模拟目标函数。该方法统一了扩散模型训练中使用的分数匹配损失和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。它通过静态熵正则化最优传输（或小批量近似），在无需模拟所学习随机过程的情况下高效学习薛定谔桥。我们发现，[SF]²M在求解薛定谔桥问题时比现有基于模拟的方法更高效且更精确。最后，我们将[SF]²M应用于从快照数据学习细胞动力学的问题。值得注意的是，[SF]²M是首个能够准确建模高维细胞动力学的方法，并能从模拟数据中恢复已知的基因调控网络。