GeodesicNVS: Probability Density Geodesic Flow Matching for Novel View Synthesis

Recent advances in generative modeling have substantially enhanced novel view synthesis, yet maintaining consistency across viewpoints remains challenging. Diffusion-based models rely on stochastic noise-to-data transitions, which obscure deterministic structures and yield inconsistent view predictions. We advocate a Data-to-Data Flow Matching framework that learns deterministic transformations between paired views, enhancing view-consistent synthesis through explicit data coupling. Building on this, we propose Probability Density Geodesic Flow Matching (PDG-FM), which aligns interpolation trajectories with density-based geodesics of a data manifold. To enable tractable geodesic estimation, we employ a teacher-student framework that distills density-based geodesic interpolants into an efficient ambient-space predictor. Empirically, our method surpasses diffusion-based baselines on Objaverse and GSO30 datasets, demonstrating improved structural coherence and smoother transitions across views. These results highlight the advantages of incorporating data-dependent geometric regularization into deterministic flow matching for consistent novel view generation.