# Graph Neural Diffusion via Generalized Opinion Dynamics

arXiv: https://arxiv.org/abs/2508.11249 · HTML: https://mlsanity.com/paper/2508.11249/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 70 references that are in the map.
- First posted on arXiv 15 Aug 2025.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [Weisfeiler and Lehman Go Cellular: CW Networks](https://mlsanity.com/paper/2106.12575/) (2021)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [Training Graph Neural Networks with 1000 Layers](https://mlsanity.com/paper/2106.07476/) (2021)
- [Edge Directionality Improves Learning on Heterophilic Graphs](https://mlsanity.com/paper/2305.10498/) (2023)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [Deep Graph Representation Learning and Optimization for Influence Maximization](https://mlsanity.com/paper/2305.02200/) (2023)
- [Graph Neural Convection-Diffusion with Heterophily](https://mlsanity.com/paper/2305.16780/) (2023)
- [Feature Transportation Improves Graph Neural Networks](https://mlsanity.com/paper/2307.16092/) (2023)
- [Maximizing Influence with Graph Neural Networks](https://mlsanity.com/paper/2108.04623/) (2021)
- [Depth-Adaptive Graph Neural Networks via Learnable Bakry-'Emery Curvature](https://mlsanity.com/paper/2503.01079/) (2025)
- [Time-aware Random Walk Diffusion to Improve Dynamic Graph Learning](https://mlsanity.com/paper/2211.01214/) (2022)
- [DRGCN: Dynamic Evolving Initial Residual for Deep Graph Convolutional Networks](https://mlsanity.com/paper/2302.05083/) (2023)
- [Effects of Stubbornness on Opinion Dynamics](https://mlsanity.com/paper/2208.04160/) (2022)
- [How Expressive are Graph Neural Networks in Recommendation?](https://mlsanity.com/paper/2308.11127/) (2023)
- [UniGO: A Unified Graph Neural Network for Modeling Opinion Dynamics on Graphs](https://mlsanity.com/paper/2502.11519/) (2025)
- [Influence Maximization in Social Networks: A Survey](https://mlsanity.com/paper/2309.04668/) (2023)

## Built on by (most cited first, 1 of 1)

- [Adaptive Initial Residual Connections for GNNs with Theoretical Guarantees](https://mlsanity.com/paper/2511.06598/) (2025)

## Abstract (arXiv)

There has been a growing interest in developing diffusion-based Graph Neural Networks (GNNs), building on the connections between message passing mechanisms in GNNs and physical diffusion processes. However, existing methods suffer from three critical limitations: (1) they rely on homogeneous diffusion with static dynamics, limiting adaptability to diverse graph structures; (2) their depth is constrained by computational overhead and diminishing interpretability; and (3) theoretical understanding of their convergence behavior remains limited. To address these challenges, we propose GODNF, a Generalized Opinion Dynamics Neural Framework, which unifies multiple opinion dynamics models into a principled, trainable diffusion mechanism. Our framework captures heterogeneous diffusion patterns and temporal dynamics via node-specific behavior modeling and dynamic neighborhood influence, while ensuring efficient and interpretable message propagation even at deep layers. We provide a rigorous theoretical analysis demonstrating GODNF's ability to model diverse convergence configurations. Extensive empirical evaluations of node classification and influence estimation tasks confirm GODNF's superiority over state-of-the-art GNNs.