mlsanityData to 7 Oct 2026

Graph Neural Reaction Diffusion Models

arXiv 2406.10871 ↗First posted 16 Jun 2024cs.LGcited by 6

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

The integration of Graph Neural Networks (GNNs) and Neural Ordinary and Partial Differential Equations has been extensively studied in recent years. GNN architectures powered by neural differential equations allow us to reason about their behavior, and develop GNNs with desired properties such as controlled smoothing or energy conservation. In this paper we take inspiration from Turing instabilities in a Reaction Diffusion (RD) system of partial differential equations, and propose a novel family of GNNs based on neural RD systems. We textcolorblackdemonstrate that our RDGNN is powerful for the modeling of various data types, from homophilic, to heterophilic, and spatio-temporal datasets. We discuss the theoretical properties of our RDGNN, its implementation, and show that it improves or offers competitive performance to state-of-the-art methods.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 57 of its 106 references that are in the map. First posted on arXiv 16 Jun 2024.

Builds on

57 of 106 references.

References · 57

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38 more
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50 most cited of 57 All 57 (JSON)

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 3; 2026: 2.

6 papers.

  1. 2024FSW-GNN: A Bi-Lipschitz WL-Equivalent Graph Neural Networkcited by 8
  2. 2025Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learningcited by 3
  3. 2026Beyond ReLU: Bifurcation, Oversmoothing, and Topological Priorscited by 2
  4. 2025Graph Flow Matching: Enhancing Image Generation with Neighbor-Aware Flow Fieldscited by 1
  5. 2025Graph Neural Regularizers for PDE Inverse Problemscited by 1
  6. 2026From Diffusion to Reaction-Diffusion: A Dynamical-Systems View of Oversmoothing in Hypergraph Neural Networkscited by 0

Similar, not cited

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  2. 2020Why Adversarial Interaction Creates Non-Homogeneous Patterns: A Pseudo-Reaction-Diffusion Model for Turing Instability
  3. 2024Towards understanding Diffusion Models (on Graphs)
  4. 2024Diffusion models as probabilistic neural operators for recovering unobserved states of dynamical systems
  5. 2025Simple Graph Contrastive Learning via Fractional-order Neural Diffusion Networks
  6. 2026Physics-Informed Neural Networks for Biological 2D+t Reaction-Diffusion Systems
  7. 2023An axiomatized PDE model of deep neural networks
  8. 2024Physics Informed Distillation for Diffusion Models