Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptation

Recent advances in cross-modal few-shot adaptation treat visual-semantic alignment as a continuous feature transport problem via Flow Matching (FM). However, we argue that Euclidean-based FM overlooks fundamental limitations of flat geometry, where polynomial volume growth fails to accommodate diverse feature distributions, leading to severe path entanglement. To this end, we propose path-decoupled Hyperbolic Flow Matching (HFM), leveraging the Lorentz manifold's exponential expansion for trajectory decoupling. HFM structures the transport via two key designs: 1) Centripetal hyperbolic alignment: It constructs a centripetal hierarchy by anchoring textual roots, which pushes visual leaves to the boundary to initialize orderly flows. 2) Path-decoupled objective: It acts as a "semantic guardrail" rigidly confining trajectories within isolated class-specific geodesic corridors via step-wise supervision. Furthermore, we devise an adaptive diameter-based stopping to prevent over-transportation into the crowded origin based on the intrinsic semantic scale. Extensive ablations on 11 benchmarks have shown that HFM establishes a new state-of-the-art, consistently outperforming its Euclidean counterparts. Our codes and models will be released.

Pretrained vision-language models have shown strong generalization ability, but adapting them to specialized visual recognition tasks with only a few labeled examples remains challenging. A key difficulty is that visual and textual representations may follow ambiguous or overlapping adaptation paths, which can reduce class discrimination when categories are visually or semantically close. This paper studies this problem from a geometric perspective and proposes Hyperbolic Flow Matching, a method that performs feature adaptation in a curved representation space rather than a conventional flat space. The proposed geometry provides more capacity for separating different semantic categories, while the learned transport process guides visual features toward their corresponding textual representations in a more structured manner. This design helps reduce undesired interactions between adaptation paths and improves the reliability of few-shot learning. Extensive experiments across multiple image classification benchmarks show that the method consistently improves over strong adaptation baselines. These results suggest that geometric structure is an important factor for improving data-efficient vision-language adaptation.