# MeshFlow Generates 3D Triangle Meshes 18× Faster Using Equivariant Flow Matching

_Research · published 2026-06-25_

Researchers from CityUHK, Stanford, Cornell Tech, and UT Austin have introduced MeshFlow, a diffusion-based generative model that produces 3D triangle meshes directly as unordered triangle soups rather than serializing geometry into long autoregressive sequences. The model employs equivariant flow matching to respect the inherent symmetries of mesh representations—permutation invariance of faces and of vertices within each face—through a modified Diffusion Transformer architecture called EquiDiT that operates without positional encodings that would break equivariance.

A key contribution is a nested optimal-transport training objective that resolves vertex-level correspondences inside candidate face matches before solving the face-level assignment, eliminating supervision signals tied to arbitrary orderings and improving convergence. The result is mesh quality comparable to state-of-the-art autoregressive generators at roughly 18× faster inference. The work is accepted to SIGGRAPH 2026, with noted limitations including the O(N³) cost of the Hungarian algorithm for large meshes and occasional generation artifacts requiring post-processing.

## Sources
- [qiisun.github.io](https://qiisun.github.io/MeshFlow/)
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