MeshFlow: Mesh Generation with Equivariant Flow Matching

2026-06-22

AI Summary

Direct generation of triangular meshes faces significant challenges in modeling the permutation symmetries of faces and their constituent vertices, and conventional autoregressive approaches suffer from low efficiency. This work proposes an equivariant optimal transport flow matching model that directly generates unordered triangle soups, thereby circumventing sequential modeling and rigorously preserving equivariance under arbitrary permutations of faces and their internal vertices. To this end, we introduce a mesh-specific equivariant Diffusion Transformer architecture and employ an optimal transport–based training objective that eliminates symmetry-breaking supervisory signals. Experimental results demonstrate that our method achieves generation quality on par with state-of-the-art autoregressive models while offering approximately 18× faster inference speed.

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/.

Problem

• mesh generation
• permutation invariance
• equivariance
• 3D representation
• symmetry

Innovation

• equivariant flow matching
• mesh generation
• optimal transport
• Diffusion Transformer
• triangle soup