Direct Product Flow Matching: Decoupling Radial and Angular Dynamics for Few-Shot Adaptation

ArXi:2605.05054v1 Announce Type: cross Recent flow matching (FM) methods improve the few-shot adaptation of vision-language models, by modeling cross-modal alignment as a continuous multi-step flow. In this paper, we argue that existing FM methods are inherently constrained by incompatible geometric priors on pre-trained cross-modal features, resulting in suboptimal adaptation performance. We first analyze these methods from a polar decomposition perspective (i.e., radial and angular sub-manifolds.