Fine-Tuning Flow Matching via Maximum Likelihood Estimation of Reconstructions

Flow Matching (FM) models achieve remarkable results in generative tasks. Building upon diffusion models, FM's simulation-free training paradigm enables simplicity and efficiency but introduces a train-inference gap: model outputs cannot be assessed during training. Moreover, the straight flow assumption suffers from some inherent limitations. To address this, we propose to fine-tune FM via Maximum Likelihood Estimation (MLE) of reconstructions -- enabled by FM's smooth ODE formulation, unlike the stochastic differential equations (SDEs) in diffusion models. We first theoretically analyze the relationship between training loss and inference error in FM under numerical precision constraints. We then propose an easy-to-implement fine-tuning framework based on MLE of reconstructions, with flexibility for sophisticated extensions. Building on this, we incorporate a generalized artificial viscosity term that enhances flow stability and robustness, accompanied by a direct parameterization method and rigorous theoretical guarantees. Experiments demonstrate our method's effectiveness across diverse settings: a toy example provides mechanistic insights into the fine-tuning process, while large-scale evaluations on meteorological forecasting and robotic manipulation policies validate reliable performance improvements.