MeshFlow: 使用等變流匹配的網格生成

摘要

網格是最常見的3D場景表示方式之一，但直接生成網格極具挑戰性，因為此表示法包含重要的對稱性，例如面與頂點的置換不變性。MeshFlow 學習直接將三角形網格生成為三角形集合，避免了將網格序列化為長自迴歸序列的需求。我們採用等變最優傳輸流匹配模型，以尊重三角形集合的關鍵對稱性：面的任意置換以及每個面內頂點的置換。為此，我們提出了一種簡單而有效的擴散變壓器架構修改，從而得到一個可擴展的網路，能夠在維持所需等變性的同時建模速度場。我們進一步引入基於最優傳輸的訓練目標，透過消除違反這些對稱性的監督信號來改善收斂性。MeshFlow 在網格品質上可與最先進的自迴歸網格生成器相媲美，同時在推理時提供約18倍的加速。專案頁面位於 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/.