(Mesh Silksong)
Topology-Preserved Auto-regressive Mesh Generation in the Manner of Weaving Silk

ICLR 2026

Gaochao Song1,2, Zibo Zhao3, Haohan Weng3, Jingbo Zeng1,2, Rongfei Jia4, Shenghua Gao1,2
1University of Hong Kong, 2Shenzhen Loop Area Institute, 3Tencent Hunyuan 3D, 4Math Magic
Paper Code 🤗 Check Points

Meshes generated by our method. Vertices are colored based on different connected component of mesh. Our method is connected component aware based on special tokens when generating, which helps capture small but critical parts of mesh.

Abstract

Existing auto-regressive mesh generation approaches suffer from ineffective topology preservation, which is crucial for practical applications. This limitation stems from previous mesh tokenization methods treating meshes as simple collections of equivalent triangles, lacking awareness of the overall topological structure during generation. To address this issue, we propose a novel mesh tokenization algorithm that provides a canonical topological framework through vertex layering and ordering, ensuring critical geometric properties including manifoldness, watertightness, face normal consistency, and part awareness in the generated meshes. Measured by Compression Ratio and Bits-per-face, we also achieved state-of-the-art compression efficiency. Furthermore, we introduce an online non-manifold data processing algorithm and a training resampling strategy to expand the scale of trainable dataset and avoid costly manual data curation. Experimental results demonstrate the effectiveness of our approach, showcasing not only intricate mesh generation but also significantly improved geometric integrity.

 

Gallery

Mesh generated conditioned on point cloud. Left mouse: change view; Right mouse: move mesh.

 

Algorithm Pipeline

 

1. Vertices Layering and Sorting

silksong scheme1

The mesh vertex for layer \( L\) with order \( i\) is denoted as \( \mathcal{V}_i^L\). Given start half-edge \(\mathcal{V}_1^0\)-\(\mathcal{V}_1^1\), the vertices' layer are easily obtained based on the graph distance to \(\mathcal{V}_1^0\) via BFS algorithm. After layering, the vertices' order in layer \( L+1\) are obtained based on local order of vertices in layer \( L\). The vertices' order of first layer can be obtained based on the start half-edge, and since the vertices' order of layer \( L+1\) can be derived from layer \( L\), the remaining vertices' order can be determined through mathematical induction.

2. Layer Adjacency Matrices Compression

silksong scheme2

All topological connections can be represented by two type of 0-1 matrices: the self-layer matrix \( \mathcal{S}_L\) and the between-layer matrix \( \mathcal{B}_L\). Suppose layer \( L\) contains \( M\) vertices and layer \( L-1\) contains \( N\) vertices. The \( \mathcal{S}_L \) with shape \( M \times M\) represents connections between vertices within layer \( L\), while \( \mathcal{B}_L \) with shape \( M \times N\) represents the connections between vertices in layer \( L\) and layer \( L-1\). We use two different algorithms to compress these matrices to tokens efficiently.

3. Token Packing

silksong scheme3

For a mesh with \( N_C\) connected components, the above algorithm will be executed \( N_C\) times. To obtain the final token representation of a mesh, we use special tokens "C" and "E" to distinguish different connected components, and token "U" to separate different layers within the same connected component. A vertex's coordinate token and its corresponding matrices tokens are packed together to facilitate better pattern learning by the autoregressive model.

 

Comparation

Comparison with other methods

Qualitative Comparison on EdgeRunner*, TreeMeshGPT, BPT, DeepMesh and our method. The * denotes faithful training on the same dataset as ours. The connected components of our generated meshes are colored since our model is connected component aware based on token "C" and can capture details for minute connected components.

(1) For tree-traversal methods EdgeRunner* and TreeMeshGPT, the manifold topology for generated mesh is guaranteed, while our method demonstrates more robust generation capability and generates more details.

(2) We achieved comparable visual results compared to local patch methods BPT and DeepMesh. However, these methods can not generate meshes with manifold topology, which hinders practical application. The non-manifold edges are colored with red for BPT and DeepMesh.

Acknowledgement

We especially thank Math Magic 's strong support for this work.

Citation


@inproceedings{songtopology,
  title={Topology-Preserved Auto-regressive Mesh Generation in the Manner of Weaving Silk},
  author={Song, Gaochao and Zhao, Zibo and Weng, Haohan and Zeng, Jingbo and Jia, Rongfei and Gao, Shenghua},
  booktitle={The Fourteenth International Conference on Learning Representations},
  year={2026}
}