# SpaceMesh: A Continuous Representation for Learning Manifold Surface Meshes

arXiv: https://arxiv.org/abs/2409.20562 · HTML: https://mlsanity.com/paper/2409.20562/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 70 references that are in the map.
- First posted on arXiv 30 Sep 2024.

## Builds on (most cited first, 30 of 34)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Point-E: A System for Generating 3D Point Clouds from Complex Prompts](https://mlsanity.com/paper/2212.08751/) (2022)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [Point-Voxel CNN for Efficient 3D Deep Learning](https://mlsanity.com/paper/1907.03739/) (2019)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018)
- [Mesh Graphormer](https://mlsanity.com/paper/2104.00272/) (2021)
- [DatasetGAN: Efficient Labeled Data Factory with Minimal Human Effort](https://mlsanity.com/paper/2104.06490/) (2021)
- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [Learning to Predict 3D Objects with an Interpolation-based Differentiable Renderer](https://mlsanity.com/paper/1908.01210/) (2019)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [MeshAnything: Artist-Created Mesh Generation with Autoregressive Transformers](https://mlsanity.com/paper/2406.10163/) (2024)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [Points2Surf: Learning Implicit Surfaces from Point Cloud Patches](https://mlsanity.com/paper/2007.10453/) (2020)
- [Image GANs meet Differentiable Rendering for Inverse Graphics and Interpretable 3D Neural Rendering](https://mlsanity.com/paper/2010.09125/) (2020)
- [POCO: Point Convolution for Surface Reconstruction](https://mlsanity.com/paper/2201.01831/) (2022)
- [Neural Dual Contouring](https://mlsanity.com/paper/2202.01999/) (2022)
- [Deformable Shape Completion with Graph Convolutional Autoencoders](https://mlsanity.com/paper/1712.00268/) (2017)
- [Neural Subdivision](https://mlsanity.com/paper/2005.01819/) (2020)
- [Point2Mesh: A Self-Prior for Deformable Meshes](https://mlsanity.com/paper/2005.11084/) (2020)
- [Meshing Point Clouds with Predicted Intrinsic-Extrinsic Ratio Guidance](https://mlsanity.com/paper/2007.09267/) (2020)

## Built on by (most cited first, 20 of 20)

- [Scaling Mesh Generation via Compressive Tokenization](https://mlsanity.com/paper/2411.07025/) (2024)
- [CAD-Llama: Leveraging Large Language Models for Computer-Aided Design Parametric 3D Model Generation](https://mlsanity.com/paper/2505.04481/) (2025)
- [FastMesh: Efficient Artistic Mesh Generation via Component Decoupling](https://mlsanity.com/paper/2508.19188/) (2025)
- [BrepGPT: Autoregressive B-rep Generation with Voronoi Half-Patch](https://mlsanity.com/paper/2511.22171/) (2025)
- [DMesh++: An Efficient Differentiable Mesh for Complex Shapes](https://mlsanity.com/paper/2412.16776/) (2024)
- [ARMesh: Autoregressive Mesh Generation via Next-Level-of-Detail Prediction](https://mlsanity.com/paper/2509.20824/) (2025)
- [MeshFlow: Efficient Artistic Mesh Generation via MeshVAE and Flow-based Diffusion Transformer](https://mlsanity.com/paper/2606.04621/) (2026)
- [TetWeave: Isosurface Extraction using On-The-Fly Delaunay Tetrahedral Grids for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2505.04590/) (2025)
- [ART-DECO: Arbitrary Text Guidance for 3D Detailizer Construction](https://mlsanity.com/paper/2505.20431/) (2025)
- [LATO.2: Factorized 3D Mesh Generation with Vertex and Topology Flow](https://mlsanity.com/paper/2607.10623/) (2026)
- [Nexus: Native Mesh Generation with Diffusion](https://mlsanity.com/paper/2607.13563/) (2026)
- [MeshFlow: Mesh Generation with Equivariant Flow Matching](https://mlsanity.com/paper/2606.23489/) (2026)
- [Meshy T2: Fast Native Mesh Generation with Flow Matching](https://mlsanity.com/paper/2607.28675/) (2026)
- [QuadLink: Autoregressive Quad-Dominant Mesh Generation via Point-Relation Learning](https://mlsanity.com/paper/2605.16813/) (2026)
- [PolyFlow: Continuous Topology Embedding Flow Matching for Artist-style Mesh Generation](https://mlsanity.com/paper/2606.30673/) (2026)
- [Learning to Build Shapes by Extrusion](https://mlsanity.com/paper/2601.22858/) (2026)
- [SQuadGen: Generating Simple Quad Layouts via Chart Distance Fields](https://mlsanity.com/paper/2604.27329/) (2026)
- [PartMat: Material-Aware 3D Part Decomposition with a Single Global Latent](https://mlsanity.com/paper/2608.01825/) (2026)
- [Inverse Rendering for Modeling with Line Primitives](https://mlsanity.com/paper/2609.00625/) (2026)
- [MeshOctave: Vertex Split-and-Rewire Cascades for Native Mesh Generation](https://mlsanity.com/paper/2609.38985/) (2026)

## Abstract (arXiv)

Meshes are ubiquitous in visual computing and simulation, yet most existing machine learning techniques represent meshes only indirectly, e.g. as the level set of a scalar field or deformation of a template, or as a disordered triangle soup lacking local structure. This work presents a scheme to directly generate manifold, polygonal meshes of complex connectivity as the output of a neural network. Our key innovation is to define a continuous latent connectivity space at each mesh vertex, which implies the discrete mesh. In particular, our vertex embeddings generate cyclic neighbor relationships in a halfedge mesh representation, which gives a guarantee of edge-manifoldness and the ability to represent general polygonal meshes. This representation is well-suited to machine learning and stochastic optimization, without restriction on connectivity or topology. We first explore the basic properties of this representation, then use it to fit distributions of meshes from large datasets. The resulting models generate diverse meshes with tessellation structure learned from the dataset population, with concise details and high-quality mesh elements. In applications, this approach not only yields high-quality outputs from generative models, but also enables directly learning challenging geometry processing tasks such as mesh repair.