Daily Paper Briefing

Abstract Overview

MeshFlow is a generative model that directly synthesizes triangle meshes as continuous triangle soups rather than relying on intermediate shape representations or autoregressive serialization. The method is built around equivariant optimal-transport flow matching so that training and generation respect two key symmetries of triangle soups: permutation of faces and permutation of vertices within each face. To support this, the paper introduces a modified diffusion transformer architecture that performs attention at the face level while preserving vertex-level equivariance, along with a symmetry-aware nested coupling objective. Experiments on ShapeNet categories evaluate distribution similarity, topological quality, ablations, and inference efficiency against autoregressive and diffusion-based baselines.

Novelty

The distinctive contribution is the adaptation of equivariant optimal-transport flow matching to direct mesh generation in a triangle-soup representation. The paper also proposes a specialized equivariant DiT block and a nested optimal-transport coupling/loss that explicitly handle the hierarchical symmetries of faces and within-face vertex orderings.

Results

Across four ShapeNet categories, MeshFlow attains mesh-generation quality comparable to strong autoregressive methods and reports the best 1-NNA in three of four categories. Relative to the diffusion baseline PolyDiff, it shows better quantitative quality and fewer self-intersections, and its inference time is reported as sub-second at 0.877 s versus 16.271 s for MeshGPT and 28.931 s for MeshXL, about an 18.55× speedup over autoregressive methods. The proposed post-processing further reduces self-intersection rates by roughly 56% on average while adding only 0.0233 s of latency.

Key Points

1. MeshFlow generates meshes directly as continuous triangle soups and explicitly models face and within-face permutation symmetries.
2. The method combines an equivariant DiT architecture with nested optimal-transport flow-matching objectives to improve convergence and produce straighter transport paths.
3. Experiments show competitive mesh quality with much faster inference than autoregressive baselines, while post-processing substantially improves topological cleanliness.

References

• arXiv: https://arxiv.org/abs/2606.23489v1
• Fugu-MT: https://fugumt.com/fugumt/paper_check/2606.23489v1
• Hugging Face Papers: https://huggingface.co/papers/2606.23489
• Project: https://qiisun.github.io/MeshFlow