mlsanityData to 7 Oct 2026

GRAND: Graph Neural Diffusion

arXiv 2106.10934 ↗First posted 21 Jun 2021cs.LG stat.MLcited by 258

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Abstract (arXiv)

We present Graph Neural Diffusion (GRAND) that approaches deep learning on graphs as a continuous diffusion process and treats Graph Neural Networks (GNNs) as discretisations of an underlying PDE. In our model, the layer structure and topology correspond to the discretisation choices of temporal and spatial operators. Our approach allows a principled development of a broad new class of GNNs that are able to address the common plights of graph learning models such as depth, oversmoothing, and bottlenecks. Key to the success of our models are stability with respect to perturbations in the data and this is addressed for both implicit and explicit discretisation schemes. We develop linear and nonlinear versions of GRAND, which achieve competitive results on many standard graph benchmarks.

Key facts. Cited by 258 papers in the map (data through 7 Oct 2026). Builds on 39 of its 68 references that are in the map. First posted on arXiv 21 Jun 2021.

Builds on

39 of 68 references.

References · 39

  1. 2017Attention Is All You Needcited by 59,932
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  4. 2017Graph Attention Networkscited by 8,854
  5. 2017Inductive Representation Learning on Large Graphscited by 6,284
  6. 2014Neural Machine Translation by Jointly Learning to Align and Translatecited by 4,530
  7. 2018Neural Ordinary Differential Equationscited by 3,733
  8. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  9. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  10. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,414
  11. 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,148
  12. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
27 more
  1. 2018Pitfalls of Graph Neural Network Evaluationcited by 994
  2. 2015Image-based Recommendations on Styles and Substitutescited by 702
  3. 2020On the Bottleneck of Graph Neural Networks and its Practical Implicationscited by 624
  4. 2016Adaptive Computation Time for Recurrent Neural Networkscited by 479
  5. 2016Geometric deep learning on graphs and manifolds using mixture model CNNscited by 468
  6. 2019Diffusion Improves Graph Learningcited by 414
  7. 2019Augmented Neural ODEscited by 396
  8. 2018Tune: A Research Platform for Distributed Model Selection and Trainingcited by 395
  9. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 343
  10. 2015Diffusion-Convolutional Neural Networkscited by 268
  11. 2020Scalable Gradients for Stochastic Differential Equationscited by 264
  12. 2019Revisiting Graph Neural Networks: All We Have is Low-Pass Filterscited by 260
  13. 2015Deep Convolutional Networks on Graph-Structured Datacited by 246
  14. 2020How to train your neural ODE: the world of Jacobian and kinetic regularizationcited by 228
  15. 2017CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filterscited by 203
  16. 2019Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limitcited by 168
  17. 2017Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equationscited by 158
  18. 2019Graph Neural Ordinary Differential Equationscited by 153
  19. 2020Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Predictioncited by 137
  20. 2019Continuous Graph Neural Networkscited by 114
  21. 2019Hamiltonian Graph Networks with ODE Integratorscited by 107
  22. 2019Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noisecited by 98
  23. 2020Implicit Graph Neural Networkscited by 98
  24. 2020Learning Differential Equations that are Easy to Solvecited by 81
  25. 2019LanczosNet: Multi-Scale Deep Graph Convolutional Networkscited by 73
  26. 2020Continuous-in-Depth Neural Networkscited by 40
  27. 2019Discrete and Continuous Deep Residual Learning Over Graphscited by 13

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 12; 2022: 42; 2023: 59; 2024: 55; 2025: 47; 2026: 43.

258 papers.

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  1. 2023A Survey on Oversmoothing in Graph Neural Networkscited by 246
  2. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 208
  3. 2022Graph-Coupled Oscillator Networkscited by 123
  4. 2022Physics-Informed Deep Neural Operator Networkscited by 110
  5. 2021PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equationscited by 106
  6. 2023DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusioncited by 85
  7. 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
  8. 2022A Survey on Graph Representation Learning Methodscited by 66
  9. 2021On the Unreasonable Effectiveness of Feature propagation in Learning on Graphs with Missing Node Featurescited by 62
  10. 2022Understanding convolution on graphs via energiescited by 58
  11. 2022Anti-Symmetric DGN: a stable architecture for Deep Graph Networkscited by 58
  12. 2022Provably expressive temporal graph networkscited by 56
38 more
  1. 2022GREAD: Graph Neural Reaction-Diffusion Networkscited by 54
  2. 2022Gradient Gating for Deep Multi-Rate Learning on Graphscited by 49
  3. 2022Equivariant Hypergraph Diffusion Neural Operatorscited by 45
  4. 2023A Fractional Graph Laplacian Approach to Oversmoothingcited by 45
  5. 2025On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learningcited by 42
  6. 2022ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networkscited by 31
  7. 2024A Review of Graph Neural Networks in Epidemic Modelingcited by 31
  8. 2022On the Robustness of Graph Neural Diffusion to Topology Perturbationscited by 30
  9. 2022Optimization-Induced Graph Implicit Nonlinear Diffusioncited by 28
  10. 2023Deep Graph Representation Learning and Optimization for Influence Maximizationcited by 27
  11. 2023Graph Neural Convection-Diffusion with Heterophilycited by 26
  12. 2023From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyondcited by 26
  13. 2023Graph Deep Learning for Time Series Forecastingcited by 26
  14. 2024On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systemscited by 26
  15. 2024Long Range Propagation on Continuous-Time Dynamic Graphscited by 26
  16. 2025Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraintscited by 26
  17. 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 25
  18. 2023Towards Deep Attention in Graph Neural Networks: Problems and Remediescited by 24
  19. 2023Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approachcited by 24
  20. 2022Graph Anomaly Detection with Graph Neural Networks: Current Status and Challengescited by 23
  21. 2023Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreachingcited by 23
  22. 2022Geometric Knowledge Distillation: Topology Compression for Graph Neural Networkscited by 22
  23. 2023Exposition on over-squashing problem on GNNs: Current Methods, Benchmarks and Challengescited by 22
  24. 2022Scalable algorithms for physics-informed neural and graph networkscited by 21
  25. 2021Evaluating Deep Graph Neural Networkscited by 19
  26. 2022Improving Graph Neural Networks with Learnable Propagation Operatorscited by 19
  27. 2023Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classificationcited by 19
  28. 2021Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networkscited by 18
  29. 2022RobustLoc: Robust Camera Pose Regression in Challenging Driving Environmentscited by 18
  30. 2023Multiscale Graph Neural Network Autoencoders for Interpretable Scientific Machine Learningcited by 18
  31. 2024PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systemscited by 18
  32. 2022Learning the Solution Operator of Boundary Value Problems using Graph Neural Networkscited by 17
  33. 2022Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approachcited by 17
  34. 2022TIDE: Time Derivative Diffusion for Deep Learning on Graphscited by 17
  35. 2024Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FRONDcited by 16
  36. 2022pathGCN: Learning General Graph Spatial Operators from Pathscited by 15
  37. 2023AbODE: Ab Initio Antibody Design using Conjoined ODEscited by 15
  38. 2023Feature Transportation Improves Graph Neural Networkscited by 15

50 most cited of 258 All 258 (JSON)