用于三维点云生成的分层流匹配

中文摘要 AI 辅助

生成高质量三维点云需要同时捕捉全局形状拓扑和局部几何细节。现有的基于流的方法依赖连续归一化流（CNF），在训练过程中需要计算成本高昂的常微分方程（ODE）求解和迹估计，而扩散模型则需要数百次迭代去噪步骤。此外，大多数方法直接在点空间采用单级生成，忽略了三维形状天然具有的分层结构。我们提出分层流匹配（HFM），将流匹配扩展为用于无条件三维点云生成的双级结构。HFM通过最优传输流匹配将任务分解为两个级别：\textit{潜在流匹配}在紧凑潜在空间中建模全局形状流形，\textit{条件点流匹配}基于潜在代码重建详细点云。两种流均采用简单的均方误差（MSE）回归损失进行训练。所得的最优传输（OT）直线路径使每个流仅需15次欧拉步即可实现高效采样，而结构化潜在空间还支持分类等下游任务。在ShapeNet和ModelNet基准上开展的大量实验表明，HFM与现有最先进方法相比取得了具有竞争力甚至更优的性能。

英文摘要

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.

发表机构

• Shandong Normal University（山东师范大学）
• University of Macau（澳门大学）

机构由 AI 辅助整理，请以论文原文为准。