mlsanityData to 13 Oct 2026

DiffusionNet: Discretization Agnostic Learning on Surfaces

arXiv 2012.00888 ↗First posted 1 Dec 2020cs.CV cs.CG cs.LGcited by 163

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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.

Key facts. Cited by 163 papers in the map (data through 13 Oct 2026). First posted on arXiv 1 Dec 2020.

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2021: 7; 2022: 26; 2023: 31; 2024: 32; 2025: 35; 2026: 32.

163 papers.

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  1. 2023MeshGPT: Generating Triangle Meshes with Decoder-Only Transformerscited by 257
  2. 2024Operator Learning: Algorithms and Analysiscited by 85
  3. 20223D-LDM: Neural Implicit 3D Shape Generation with Latent Diffusion Modelscited by 67
  4. 2021Subdivision-Based Mesh Convolution Networkscited by 60
  5. 2021DPFM: Deep Partial Functional Mapscited by 58
  6. 2023Unsupervised Learning of Robust Spectral Shape Matchingcited by 57
  7. 2023Swallowing the Bitter Pill: Simplified Scalable Conformer Generationcited by 55
  8. 2022Unsupervised Deep Multi-Shape Matchingcited by 39
  9. 2022Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matchingcited by 36
  10. 2022Learning Multi-resolution Functional Maps with Spectral Attention for Robust Shape Matchingcited by 35
  11. 2024An Object is Worth 64x64 Pixels: Generating 3D Object via Image Diffusioncited by 34
  12. 20223D Highlighter: Localizing Regions on 3D Shapes via Text Descriptionscited by 32
38 more
  1. 2021Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronizationcited by 30
  2. 2023Spatially and Spectrally Consistent Deep Functional Mapscited by 30
  3. 2022Mesh Neural Networks for SE(3)-Equivariant Hemodynamics Estimation on the Artery Wallcited by 29
  4. 2025ARTalk: Speech-Driven 3D Head Animation via Autoregressive Modelcited by 29
  5. 2022Neural Jacobian Fields: Learning Intrinsic Mappings of Arbitrary Meshescited by 28
  6. 2024Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolationcited by 26
  7. 2023Neural Face Rigging for Animating and Retargeting Facial Meshes in the Wildcited by 25
  8. 2024ScanTalk: 3D Talking Heads from Unregistered Scanscited by 24
  9. 2023Self-Supervised Learning for Multimodal Non-Rigid 3D Shape Matchingcited by 23
  10. 2022Intrinsic Neural Fields: Learning Functions on Manifoldscited by 20
  11. 2023Understanding and Improving Features Learned in Deep Functional Mapscited by 20
  12. 2022Growing Isotropic Neural Cellular Automatacited by 19
  13. 2023NCP: Neural Correspondence Prior for Effective Unsupervised Shape Matchingcited by 18
  14. 2023Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matchingcited by 18
  15. 2022TIDE: Time Derivative Diffusion for Deep Learning on Graphscited by 17
  16. 2023Controllable Group Choreography using Contrastive Diffusioncited by 17
  17. 2024Memory-Scalable and Simplified Functional Map Learningcited by 14
  18. 2024iSeg: Interactive 3D Segmentation via Interactive Attentioncited by 14
  19. 2025Denoising Functional Maps: Diffusion Models for Shape Correspondencecited by 14
  20. 2022Implicit field supervision for robust non-rigid shape matchingcited by 13
  21. 2022SRFeat: Learning Locally Accurate and Globally Consistent Non-Rigid Shape Correspondencecited by 13
  22. 2023Interpretable statistical representations of neural population dynamics and geometrycited by 12
  23. 2023Non-Rigid Shape Registration via Deep Functional Maps Priorcited by 12
  24. 2024Integrating Efficient Optimal Transport and Functional Maps For Unsupervised Shape Correspondence Learningcited by 12
  25. 2024SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimationcited by 12
  26. 2024Wormhole Loss for Partial Shape Matchingcited by 12
  27. 2025Geometric Retargeting: A Principled, Ultrafast Neural Hand Retargeting Algorithmcited by 12
  28. 2022Laplacian2Mesh: Laplacian-Based Mesh Understandingcited by 11
  29. 2023Manifold Diffusion Fieldscited by 11
  30. 2023Single Mesh Diffusion Models with Field Latents for Texture Generationcited by 11
  31. 2024Beyond Complete Shapes: A Benchmark for Quantitative Evaluation of 3D Shape Surface Matching Algorithmscited by 11
  32. 2021DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Cloudscited by 10
  33. 2022A Flexible Diffusion Modelcited by 10
  34. 2024Zero-Shot Image Feature Consensus with Deep Functional Mapscited by 10
  35. 2024DV-Matcher: Deformation-based Non-Rigid Point Cloud Matching Guided by Pre-trained Visual Featurescited by 10
  36. 2025DiffuMatch: Category-Agnostic Spectral Diffusion Priors for Robust Non-rigid Shape Matchingcited by 10
  37. 2022What's the Situation with Intelligent Mesh Generation: A Survey and Perspectivescited by 9
  38. 2022DA Wand: Distortion-Aware Selection using Neural Mesh Parameterizationcited by 9

50 most cited of 163 All 163 (JSON)