Density-Aware Point Cloud Upsampling via Relational Graph Flow Matching

Real-world point clouds exhibit non-uniform density distributions, varying across distance and scale. Conventional upsampling methods typically treat points homogeneously, which over-smooths sparse regions while over-processing dense regions. We propose PURF, a density-aware point cloud upsampling framework based on relational graph flow matching. PURF leverages a heterogeneous graph representation to capture density variations through relational graph construction, and employs transformer-based flow matching to predict timestep-dependent velocity fields. This design enables a density-aware and efficient mapping from sparse inputs to dense point clouds, reducing computational overhead compared to recent approaches. Extensive experiments on synthetic, KITTI, and a proprietary campus dataset collected by our team demonstrate that PURF achieves advanced performance in upsampling point clouds qualitatively and quantitatively.