MeshFlow: Mesh Generation with Equivariant Flow Matching

摘要

Meshes are among the most common 3D scene representations, but directly generating meshes is challenging largely because the mesh representation contains many structures, such as permutation invariance of vertices or faces. To address this challenge, we present a novel approach that learns to generate triangle meshes represented as triangle soups. We adopt equivariant optimal-transport flow matching models that respect key symmetries within the triangle soup representation, including permutation invariance among faces and among vertices within each of the faces. Toward this goal, we propose a simple yet effective modification to the state-of-the-art Diffusion Transformer architecture, resulting in a scalable network capable of modeling a flow field while maintaining the desirable symmetries (equivariance). Moreover, we introduce a loss function grounded in optimal transport principles that improves model convergence by eliminating training signals that violate these symmetries. Our model can achieve performance comparable to state-of-the-art auto-regressive mesh generators while providing about an 18× speedup during inference.