Flow Matching Posterior Sampling: A Training-free Conditional Generation for Flow Matching

Training-free conditional generation based on flow matching aims to leverage pre-trained unconditional flow matching models to perform conditional generation without retraining. Recently, a successful training-free conditional generation approach incorporates conditions via posterior sampling, which relies on the availability of a score function in the unconditional diffusion model. However, flow matching models lack an explicit score function, rendering this strategy inapplicable. Approximate posterior sampling for flow matching has been explored, but it is limited to linear inverse problems. In this paper, we propose Flow Matching-based Posterior Sampling (FMPS) to broaden its scope of application. We introduce a correction term by steering the velocity field. This correction term can be reformulated to incorporate a surrogate score function, thereby bridging the gap between flow matching models and score-based posterior sampling. Hence, FMPS enables posterior sampling to be adjusted within the flow-matching framework. Furthermore, we propose two practical implementations of the correction mechanism: one to improve generation quality and the other to enhance computational efficiency. Experimental results on diverse conditional generation tasks demonstrate that our method achieves superior generation quality compared to existing state-of-the-art approaches, validating the effectiveness and generality of FMPS.