💡 MeshFlow is a method for generating triangle meshes directly using equivariant optimal-transport flow matching models. The problem of generating meshes is challenging due to the symmetries present in the representation, including permutation invariance of faces and vertices. Traditional autoregressive methods serialize meshes into long sequences, which can be slow and inefficient.

MeshFlow addresses this problem by learning to generate triangle meshes as triangle soups, which are unordered collections of triangles. The method uses equivariant optimal-transport flow matching models that respect the symmetries of triangle soups, including arbitrary permutations of faces and permutations of vertices within each face.

To achieve this, the authors propose a modification to the Diffusion Transformer architecture, resulting in a scalable network that can model a velocity field while maintaining the desired equivariance. The authors also introduce an optimal-transport-based training objective that improves convergence by eliminating supervision signals that violate these symmetries.

The results show that MeshFlow achieves mesh quality comparable to state-of-the-art autoregressive mesh generators, but provides a significant speedup of about 18 times during inference. This makes MeshFlow a more efficient and effective method for generating high-quality triangle meshes. Overall, the contributions of MeshFlow include a novel method for generating triangle meshes, a scalable and equivariant network architecture, and an optimal-transport-based training objective that improves convergence and mesh quality.