🤖 AI Summary
Existing 3D point cloud generation methods struggle to simultaneously capture global topology and fine local details, often relying on computationally expensive ODE solvers or multi-step denoising procedures. This work proposes a Hierarchical Flow Matching (HFM) framework that extends flow matching into a two-level structure: it first models the global shape manifold via implicit flow matching in a compact latent space, then performs conditional point flow matching—conditioned on the learned latent code—to reconstruct detailed geometry. Both stages are trained with simple MSE regression and leverage optimal transport paths with Euler integration for efficient sampling. The method achieves state-of-the-art or comparable generation quality on ShapeNet and ModelNet, producing high-fidelity point clouds with only 15 sampling steps per level, while also yielding a structured latent space amenable to downstream tasks.
📝 Abstract
Generating high-quality 3D point clouds requires capturing both global shape topology and local geometric details. Existing flow-based methods rely on continuous normalizing flows (CNFs) that demand expensive ODE solving and trace estimation during training, while diffusion models require hundreds of iterative denoising steps. Moreover, most approaches adopt single-level generation directly in point space, disregarding the hierarchical structure natural to 3D shapes. We propose Hierarchical Flow Matching (HFM) that extends flow matching to bilevel structure for unconditional 3D point cloud generation. HFM decomposes the task into two levels via optimal-transport flow matching: a \textit{Latent Flow Matching} models the global shape manifold in a compact latent space, and a \textit{Conditional Point Flow Matching} reconstructs detailed point clouds conditioned on the latent code. Both flows are trained with simple MSE regression losses. The resulting straight OT paths enable efficient sampling with as few as 15 Euler steps per flow, while the structured latent space supports downstream tasks including classification. Extensive experiments on ShapeNet and ModelNet benchmarks demonstrate that HFM achieves competitive or even best performance compared with prior state-of-the-art methods.