Continuous normalizing flows (CNFs) learn the probability path between a
reference and a target density by modeling the vector field generating said
path using neural networks. Recently, Lipman et al. (2022) introduced a simple
and inexpensive method for training CNFs in generative modeling, termed flow
matching (FM). In this paper, we re-purpose this method for probabilistic
inference by incorporating Markovian sampling methods in evaluating the FM
objective and using the learned probability path to improve Monte Carlo
sampling. We propose a sequential method, which uses samples from a Markov
chain to fix the probability path defining the FM objective. We augment this
scheme with an adaptive tempering mechanism that allows the discovery of
multiple modes in the target. Under mild assumptions, we establish convergence
to a local optimum of the FM objective, discuss improvements in the convergence
rate, and illustrate our methods on synthetic and real-world examples.

通过建模生成概率路径的向量场，连续归一化流（CNFs）利用神经网络学习参考密度与目标密度之间的概率路径。本文重新利用流匹配（FM）方法，结合马尔可夫采样方法评估 FM 目标和使用学习的概率路径改进蒙特卡洛采样，将该方法用于概率推断。我们提出了一种顺序方法，利用马尔可夫链的样本修正定义 FM 目标的概率路径。我们增加了自适应调节机制以发现目标中的多个模式。在温和的假设下，我们证明了 FM 目标的局部最优收敛性，讨论了收敛速率的改进，并在合成和真实世界示例中说明了我们的方法。