# Neural Subdivision

arXiv: https://arxiv.org/abs/2005.01819 · HTML: https://mlsanity.com/paper/2005.01819/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2020.

## Built on by (most cited first, 30 of 49)

- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [Text2Mesh: Text-Driven Neural Stylization for Meshes](https://mlsanity.com/paper/2112.03221/) (2021)
- [BRepNet: A topological message passing system for solid models](https://mlsanity.com/paper/2104.00706/) (2021)
- [TANGO: Text-driven Photorealistic and Robust 3D Stylization via Lighting Decomposition](https://mlsanity.com/paper/2210.11277/) (2022)
- [Subdivision-Based Mesh Convolution Networks](https://mlsanity.com/paper/2106.02285/) (2021)
- [3DStyleNet: Creating 3D Shapes with Geometric and Texture Style Variations](https://mlsanity.com/paper/2108.12958/) (2021)
- [Neural Marching Cubes](https://mlsanity.com/paper/2106.11272/) (2021)
- [Multi-View Mesh Reconstruction with Neural Deferred Shading](https://mlsanity.com/paper/2212.04386/) (2022)
- [3D Paintbrush: Local Stylization of 3D Shapes with Cascaded Score Distillation](https://mlsanity.com/paper/2311.09571/) (2023)
- [Neural Surface Maps](https://mlsanity.com/paper/2103.16942/) (2021)
- [MeshMAE: Masked Autoencoders for 3D Mesh Data Analysis](https://mlsanity.com/paper/2207.10228/) (2022)
- [Learning to Generate 3D Shapes from a Single Example](https://mlsanity.com/paper/2208.02946/) (2022)
- [SpaceMesh: A Continuous Representation for Learning Manifold Surface Meshes](https://mlsanity.com/paper/2409.20562/) (2024)
- [Learning Feature Aggregation for Deep 3D Morphable Models](https://mlsanity.com/paper/2105.02173/) (2021)
- [Neural Progressive Meshes](https://mlsanity.com/paper/2308.05741/) (2023)
- [What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives](https://mlsanity.com/paper/2211.06009/) (2022)
- [TetGAN: A Convolutional Neural Network for Tetrahedral Mesh Generation](https://mlsanity.com/paper/2210.05735/) (2022)
- [Learning the Geodesic Embedding with Graph Neural Networks](https://mlsanity.com/paper/2309.05613/) (2023)
- [Differentiable Visual Computing for Inverse Problems and Machine Learning](https://mlsanity.com/paper/2312.04574/) (2023)
- [Text-guided Controllable Mesh Refinement for Interactive 3D Modeling](https://mlsanity.com/paper/2406.01592/) (2024)
- [MARS: Mesh AutoRegressive Model for 3D Shape Detailization](https://mlsanity.com/paper/2502.11390/) (2025)
- [Neural Shape Compiler: A Unified Framework for Transforming between Text, Point Cloud, and Program](https://mlsanity.com/paper/2212.12952/) (2022)
- [Variational Barycentric Coordinates](https://mlsanity.com/paper/2310.03861/) (2023)
- [Neural Laplacian Operator for 3D Point Clouds](https://mlsanity.com/paper/2409.06506/) (2024)
- [ART-DECO: Arbitrary Text Guidance for 3D Detailizer Construction](https://mlsanity.com/paper/2505.20431/) (2025)
- [PhysGraph: Physics-Based Integration Using Graph Neural Networks](https://mlsanity.com/paper/2301.11841/) (2023)
- [Mesh Draping: Parametrization-Free Neural Mesh Transfer](https://mlsanity.com/paper/2110.05433/) (2021)
- [Mesh Convolution with Continuous Filters for 3D Surface Parsing](https://mlsanity.com/paper/2112.01801/) (2021)
- [UVStyle-Net: Unsupervised Few-shot Learning of 3D Style Similarity Measure for B-Reps](https://mlsanity.com/paper/2105.02961/) (2021)
- [Transfer Learning using Spectral Convolutional Autoencoders on Semi-Regular Surface Meshes](https://mlsanity.com/paper/2212.05810/) (2022)

## Abstract (arXiv)

This paper introduces Neural Subdivision, a novel framework for data-driven coarse-to-fine geometry modeling. During inference, our method takes a coarse triangle mesh as input and recursively subdivides it to a finer geometry by applying the fixed topological updates of Loop Subdivision, but predicting vertex positions using a neural network conditioned on the local geometry of a patch. This approach enables us to learn complex non-linear subdivision schemes, beyond simple linear averaging used in classical techniques. One of our key contributions is a novel self-supervised training setup that only requires a set of high-resolution meshes for learning network weights. For any training shape, we stochastically generate diverse low-resolution discretizations of coarse counterparts, while maintaining a bijective mapping that prescribes the exact target position of every new vertex during the subdivision process. This leads to a very efficient and accurate loss function for conditional mesh generation, and enables us to train a method that generalizes across discretizations and favors preserving the manifold structure of the output. During training we optimize for the same set of network weights across all local mesh patches, thus providing an architecture that is not constrained to a specific input mesh, fixed genus, or category. Our network encodes patch geometry in a local frame in a rotation- and translation-invariant manner. Jointly, these design choices enable our method to generalize well, and we demonstrate that even when trained on a single high-resolution mesh our method generates reasonable subdivisions for novel shapes.