# DiffusionNet: Discretization Agnostic Learning on Surfaces

arXiv: https://arxiv.org/abs/2012.00888 · HTML: https://mlsanity.com/paper/2012.00888/

## Key facts

- Cited by 164 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2020.

## Built on by (most cited first, 30 of 164)

- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [Operator Learning: Algorithms and Analysis](https://mlsanity.com/paper/2402.15715/) (2024)
- [3D-LDM: Neural Implicit 3D Shape Generation with Latent Diffusion Models](https://mlsanity.com/paper/2212.00842/) (2022)
- [Subdivision-Based Mesh Convolution Networks](https://mlsanity.com/paper/2106.02285/) (2021)
- [DPFM: Deep Partial Functional Maps](https://mlsanity.com/paper/2110.09994/) (2021)
- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)
- [Swallowing the Bitter Pill: Simplified Scalable Conformer Generation](https://mlsanity.com/paper/2311.17932/) (2023)
- [Unsupervised Deep Multi-Shape Matching](https://mlsanity.com/paper/2207.09610/) (2022)
- [Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matching](https://mlsanity.com/paper/2204.13453/) (2022)
- [Learning Multi-resolution Functional Maps with Spectral Attention for Robust Shape Matching](https://mlsanity.com/paper/2210.06373/) (2022)
- [An Object is Worth 64x64 Pixels: Generating 3D Object via Image Diffusion](https://mlsanity.com/paper/2408.03178/) (2024)
- [3D Highlighter: Localizing Regions on 3D Shapes via Text Descriptions](https://mlsanity.com/paper/2212.11263/) (2022)
- [Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronization](https://mlsanity.com/paper/2111.12878/) (2021)
- [Spatially and Spectrally Consistent Deep Functional Maps](https://mlsanity.com/paper/2308.08871/) (2023)
- [Mesh Neural Networks for SE(3)-Equivariant Hemodynamics Estimation on the Artery Wall](https://mlsanity.com/paper/2212.05023/) (2022)
- [ARTalk: Speech-Driven 3D Head Animation via Autoregressive Model](https://mlsanity.com/paper/2502.20323/) (2025)
- [Neural Jacobian Fields: Learning Intrinsic Mappings of Arbitrary Meshes](https://mlsanity.com/paper/2205.02904/) (2022)
- [Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation](https://mlsanity.com/paper/2402.18920/) (2024)
- [Neural Face Rigging for Animating and Retargeting Facial Meshes in the Wild](https://mlsanity.com/paper/2305.08296/) (2023)
- [ScanTalk: 3D Talking Heads from Unregistered Scans](https://mlsanity.com/paper/2403.10942/) (2024)
- [Self-Supervised Learning for Multimodal Non-Rigid 3D Shape Matching](https://mlsanity.com/paper/2303.10971/) (2023)
- [Intrinsic Neural Fields: Learning Functions on Manifolds](https://mlsanity.com/paper/2203.07967/) (2022)
- [Understanding and Improving Features Learned in Deep Functional Maps](https://mlsanity.com/paper/2303.16527/) (2023)
- [Growing Isotropic Neural Cellular Automata](https://mlsanity.com/paper/2205.01681/) (2022)
- [NCP: Neural Correspondence Prior for Effective Unsupervised Shape Matching](https://mlsanity.com/paper/2301.05839/) (2023)
- [Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matching](https://mlsanity.com/paper/2312.03678/) (2023)
- [TIDE: Time Derivative Diffusion for Deep Learning on Graphs](https://mlsanity.com/paper/2212.02483/) (2022)
- [Controllable Group Choreography using Contrastive Diffusion](https://mlsanity.com/paper/2310.18986/) (2023)
- [Memory-Scalable and Simplified Functional Map Learning](https://mlsanity.com/paper/2404.00330/) (2024)
- [iSeg: Interactive 3D Segmentation via Interactive Attention](https://mlsanity.com/paper/2404.03219/) (2024)

## Abstract (arXiv)

We introduce a new general-purpose approach to deep learning on 3D surfaces, based on the insight that a simple diffusion layer is highly effective for spatial communication. The resulting networks are automatically robust to changes in resolution and sampling of a surface -- a basic property which is crucial for practical applications. Our networks can be discretized on various geometric representations such as triangle meshes or point clouds, and can even be trained on one representation then applied to another. We optimize the spatial support of diffusion as a continuous network parameter ranging from purely local to totally global, removing the burden of manually choosing neighborhood sizes. The only other ingredients in the method are a multi-layer perceptron applied independently at each point, and spatial gradient features to support directional filters. The resulting networks are simple, robust, and efficient. Here, we focus primarily on triangle mesh surfaces, and demonstrate state-of-the-art results for a variety of tasks including surface classification, segmentation, and non-rigid correspondence.