MeshFlow: Mesh Generation with Equivariant Flow Matching

Traditional mesh generation often relies on two-stage pipelines (e.g., generating voxels or point clouds first) or autoregressive models that serialize meshes into sequences. These methods suffer from either poor mesh quality or slow inference speeds and error accumulation. This paper asks whether a flow-matching approach can generate high-quality meshes directly while maintaining the efficiency and control benefits of continuous generative models.

MeshFlow treats a mesh as a triangle soup—a collection of triangles where the order of faces and the order of vertices within each face are arbitrary. The authors identify that this representation possesses two levels of permutation invariance: face-level (the set of triangles) and vertex-level (the three vertices per triangle). To handle this, they introduce an equivariant Diffusion Transformer (DiT) architecture that maintains these symmetries by avoiding standard positional encodings. Furthermore, they propose an optimal-transport-based training objective that aligns noise and data samples to minimize distance while respecting the group symmetries, leading to straighter, more efficient trajectories during generation.

MeshFlow successfully generates high-quality 3D meshes directly from Gaussian noise. By leveraging the symmetry-aware architecture and the optimal-transport loss, the model produces meshes with quality comparable to state-of-the-art autoregressive generators. Crucially, because the model avoids the sequential generation bottleneck, it achieves an approximately 18x speedup in inference time, making it significantly more practical for real-time graphics applications.