Optical Flow Matching: Reframing Optical Flow as Continuous Transport Dynamics

Modern optical flow estimation, though empowered by deep neural architectures, remains rooted in the discrete correspondence paradigm inherited from classical vision. Most networks infer frame-to-frame displacements or correlation volumes, capturing where pixels move but not how motion evolves continuously through time. Yet physical motion in the real world follows smooth dynamics governed by underlying velocity fields, as long established in fluid mechanics and transport theory. To bridge this gap, we introduce Optical Flow Matching (OFM), a continuous formulation that learns a time-dependent velocity field to transport pixel coordinates along motion distribution coherent trajectories. A key component of our OFM is Triangle Velocities Synergy (TVS), a lightweight geometric mechanism that provides a stable and physically meaningful velocity construction, ensuring that continuous transport remains well-defined. Combined with an Euler-based ODE solver, OFM yields flow fields that are temporally smooth, geometrically consistent, and process-interpretable. Experiments on Sintel, KITTI, and Spring demonstrate that OFM achieves state-of-the-art accuracy, enhanced temporal stability, and notably stronger cross-dataset generalization, advancing optical flow estimation from correspondence inference to continuous dynamical reasoning. All code and trained models will be released upon acceptance to facilitate further research.