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.

翻译：我们提出了无模拟得分与流匹配（[SF]²M），一种无需模拟即可推断随机动力学的目标函数，适用于从任意源分布和目标分布中抽取的非配对样本。该方法统一了扩散模型训练中使用的得分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解释为薛定谔桥问题，通过静态熵正则化最优传输或小批量近似，无需模拟学习到的随机过程即可高效学习SB。我们发现[SF]²M相比以往基于模拟的方法，在求解SB问题时效率更高且解更精确。最终，我们将[SF]²M应用于从快照数据学习细胞动力学问题。值得注意的是，[SF]²M是首个能精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。