MeshFlow: Mesh Generation with Equivariant Flow Matching

Qi Sun1, Kiyohiro Nakayama2, Jing Nathan Yan3, Qixing Huang4, Alexander Rush3,
Leonidas Guibas2, Gordon Wetzstein2, Jing Liao1, and Guandao Yang4
1CityUHK 2Stanford 3Cornell Tech 4UT Austin

SIGGRAPH 2026

Paper Slides (TBD) Code HF Demo Model

Video

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× speedup during inference.

Method

Symmetries in Triangle Soups

MeshFlow represents a mesh as a triangle soup, an unordered set of triangular faces. This representation has two nested symmetries: the faces can be arbitrarily permuted, and the vertices inside each triangle can be permuted without changing the represented geometry.

Face permutation symmetry in triangle soups
Face permutation leaves the represented mesh unchanged.
Vertex permutation symmetry inside a triangle face
Vertex order inside each triangle introduces an additional local symmetry.

Nested Optimal Transport

A naive noise-data correspondence can create training signals that depend on arbitrary face and vertex orderings. MeshFlow defines the coupling cost over the orbit of the triangle soup: an inner assignment first finds the best vertex permutation for every face pair, and an outer Hungarian assignment then matches faces using these symmetry-aware costs.

Nested optimal transport coupling diagram
Nested OT reduces path crossings by resolving vertex correspondences inside each candidate face match before solving the face-level assignment.

Equivariant Diffusion Transformer

EquiDiT adapts a Diffusion Transformer-style architecture to triangle soups without using positional encodings that would break equivariance. It embeds vertices, pools them into face features, applies self-attention over unordered faces, and broadcasts the updated face context back to vertex-level predictions.

EquiDiT architecture diagram
EquiDiT performs attention over face features while preserving equivariant vertex-level predictions.

Gallery

BibTeX

@inproceedings{meshflow,
  title     = {MeshFlow: Mesh Generation with Equivariant Flow Matching},
  author    = {Sun, Qi and Nakayama, Kiyohiro and Yan, Jing Nathan and Huang, Qixing and Rush, Alexander and Guibas, Leonidas and Wetzstein, Gordon and Liao, Jing and Yang, Guandao},
  booktitle = {ACM SIGGRAPH Conference Papers},
  year      = {2026}
}