GeodesicNVS: Probability Density Geodesic Flow Matching for Novel View Synthesis

TL;DR

This work proposes a Data-to-Data Flow Matching framework that learns deterministic transformations directly between paired views, enhancing view-consistent synthesis through explicit data coupling and introduces Probability Density Geodesic Flow Matching (PDG-FM), which constrains flow trajectories using geodesic interpolants derived from probability density metrics of pretrained diffusion models.

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.

Figures (10)

• Figure 1: From Conditional Diffusion Model to Probability Density Geodesic Flow Matching. Conventional diffusion models learn stochastic noise-to-data transitions, often losing deterministic structure. We instead train a Data-to-Data Flow Matching network to learn continuous deterministic transformations between paired data samples $(x_0, x_1)$. To ensure geometric consistency, we propose to deploy a probability-density-based geodesic to aligns flow matching interpolant with high-density regions of the data manifold. This unified design couples accurate data coupling with manifold-aware regularization, yielding realistic, view-consistent transformations.
• Figure 2: Overview of the Probability Density Geodesic Flow Matching (PDG-FM) framework. (a) Data-to-Data Flow Matching learns deterministic mappings between paired samples $(x_0, x_1)$ by encoding source and target views into latent space and predicting intermediate states $x_t$ through either linear interpolants (Eq. \ref{['eq:flowMatching']}) or geodesic interpolants (Eq. \ref{['eq:geodeisc_xt']}) predicted by the GeodesicNet $\phi_\eta$. The velocity field $v_\theta(x_t, t, c)$ is conditioned on source view features and Plücker ray embeddings, and its decoded outputs yield novel views consistent with the target pose. (b) Variational Distillation of Geodesics trains GeodesicNet $\phi_\eta$ to produce manifold-aligned interpolants by minimizing path energy defined under the probability density geodesic metric $\|x\|_{\mathcal{G}(x)} = \sqrt{x^\top x / p(x)^2}$, where the density $p(x)$ is estimated using a pretrained diffusion score function (Eq. \ref{['eq:nabla_logp']}). (c) The unified PDG-FM integrates both components, resulting in geometry-aware and manifold-consistent transformations for view-consistent novel view synthesis.
• Figure 3: Qualitative comparisons on Objaverse. Comparison of Data-to-Data FM (with linear interpolant), the Noise-to-Data FM (Naive FM) baseline and the diffusion-based Free3D model.
• Figure 4: Qualitative comparisons on GSO30. Comparison of Free3D and our method (“Ours”) given the same input view.
• Figure 5: Qualitative comparisons between Geodesic FM and Linear FM on Objaverse. Visual results showing that Geodesic FM generates more geometrically faithful novel views. The improvement reflects the effect of energy-guided optimization along data-dependent geodesics.