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.

翻译：连续归一化流（CNFs）通过神经网络建模生成概率路径的向量场，从而学习参考分布与目标分布之间的概率路径。近期，Lipman等人（2022）提出了一种称为流匹配（FM）的简单且低成本的CNFs训练方法，用于生成建模。本文通过将马尔可夫采样方法融入FM目标函数评估过程，并利用学习到的概率路径改进蒙特卡洛采样，将该方法重新应用于概率推断。我们提出一种序列化方法，该方法使用马尔可夫链的样本来固定定义FM目标的概率路径。我们通过引入自适应退火机制增强该方案，使其能够发现目标分布中的多模态结构。在温和假设下，我们证明了算法对FM目标局部最优解的收敛性，讨论了收敛速率的改进，并通过合成与真实案例验证了所提方法的有效性。