MeshFlow: 基于等变流匹配的网格生成

摘要

网格是常见的3D场景表示之一，但由于其表示包含重要的对称性（如面和顶点的排列不变性），直接生成网格颇具挑战。MeshFlow学习直接以三角网格汤的形式生成三角形网格，避免了将网格序列化为冗长自回归序列的需求。我们采用等变最优传输流匹配模型，该模型尊重三角网格汤的关键对称性：面的任意排列以及每个面内顶点的排列。为实现这一目标，我们对扩散Transformer架构提出了一种简单而有效的改进，构建了一个可扩展的网络，能够在保持所需等变性的同时建模速度场。此外，我们引入了一种基于最优传输的训练目标，通过消除违反这些对称性的监督信号来改善收敛性。MeshFlow在网格质量上与最先进的自回归网格生成器相当，同时在推理过程中实现了约18倍的加速。项目页面位于https://qiisun.github.io/MeshFlow/。

English

Meshes are among the most common 3D scene representations, but directly generating meshes is challenging because the representation contains important symmetries, including permutation invariance of faces and vertices. MeshFlow learns to generate triangle meshes directly as triangle soups, avoiding the need to serialize meshes into long autoregressive sequences. We adopt equivariant optimal-transport flow matching models that respect the key symmetries of triangle soups: arbitrary permutations of faces and permutations of the vertices within each face. Toward this goal, we propose a simple yet effective modification to the Diffusion Transformer architecture, resulting in a scalable network capable of modeling a velocity field while maintaining the desired equivariance. We further introduce an optimal-transport-based training objective that improves convergence by eliminating supervision signals that violate these symmetries. MeshFlow achieves mesh quality comparable to state-of-the-art autoregressive mesh generators while providing about an 18times speedup during inference. Project page is at https://qiisun.github.io/MeshFlow/.