Overview
MeshFlow is a proposed method for directly generating triangle meshes, framing them as triangle soups. This approach addresses the inherent challenges of mesh generation, particularly concerning the symmetries present in 3D scene representations. The model utilizes equivariant optimal-transport flow matching to respect the permutation invariances associated with faces and vertices within triangle soups.
Research Context
Meshes constitute a common representation for 3D scenes. The direct generation of these meshes presents a challenge due to the specific symmetries embedded within the representation. These symmetries include the arbitrary permutation of faces and the permutation of vertices within each face. Traditional methods often involve serializing meshes into autoregressive sequences, which MeshFlow aims to circumvent.
Approach
MeshFlow's methodology focuses on generating triangle meshes directly as 'triangle soups', thereby avoiding the sequential autoregressive generation paradigm. The core of its approach involves the adoption of equivariant optimal-transport flow matching models. These models are designed to inherently respect the identified symmetries of triangle soups: specifically, arbitrary permutations of faces and permutations of vertices within individual faces.
To implement this, MeshFlow introduces a modification to the Diffusion Transformer architecture. This modification is described as simple yet effective, enabling the resulting network to model a velocity field while simultaneously maintaining the requisite equivariance. Furthermore, the system incorporates an optimal-transport-based training objective. This objective is designed to enhance convergence by explicitly eliminating supervision signals that are inconsistent with the aforementioned symmetries.
Findings
- MeshFlow achieves mesh quality that is comparable to that of current state-of-the-art autoregressive mesh generators.
- The inference process using MeshFlow demonstrates an approximate 18-fold speedup compared to state-of-the-art autoregressive mesh generators.
Why This Matters
The development of MeshFlow addresses the complexities of generating 3D scene representations by offering an alternative to autoregressive sequencing. Its ability to generate meshes directly while maintaining competitive quality and achieving substantial inference speedups suggests advancements in computational efficiency for 3D modeling tasks.