MeshFlow: Mesh Generation with Equivariant Flow Matching
2026-06-22 • Graphics
GraphicsComputer Vision and Pattern Recognition
AI summaryⓘ
The authors developed MeshFlow, a method to create 3D mesh shapes directly without breaking them into long sequences, which is usually hard because mesh parts can be arranged in many interchangeable ways. They use advanced math techniques called equivariant optimal-transport flows to respect the natural symmetries in meshes, like how faces and vertices can be swapped without changing the shape. Their approach modifies a type of neural network to better handle these symmetries and improves training by focusing only on valid patterns. MeshFlow produces high-quality meshes much faster than previous methods according to the authors.
3D MeshPermutation InvarianceTriangle MeshEquivariant ModelOptimal TransportFlow MatchingDiffusion TransformerAutoregressive ModelVelocity FieldMesh Generation
Authors
Qi Sun, Kiyohiro Nakayama, Jing Nathan Yan, Qixing Huang, Alexander Rush, Leonidas Guibas, Gordon Wetzstein, Jing Liao, Guandao Yang
Abstract
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 18$\times$ speedup during inference. Project page is at https://qiisun.github.io/MeshFlow/.