GeodesicNVS: Probability Density Geodesic Flow Matching for Novel View Synthesis

Abstract: 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 propose a Data-to-Data Flow Matching framework that learns deterministic transformations directly between paired views, enhancing view-consistent synthesis through explicit data coupling. To further enhance geometric coherence, we introduce Probability Density Geodesic Flow Matching (PDG-FM), which constrains flow trajectories using geodesic interpolants derived from probability density metrics of pretrained diffusion models. Such alignment with high-density regions of the data manifold promotes more realistic interpolants between samples. Empirically, our method surpasses diffusion-based NVS baselines, 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.