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A Generalized Neural Diffusion Framework on Graphs
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Proposes a general diffusion framework with a fidelity term that unifies GCN/SGC, APPNP, GAT, AMP and DAGNN, and derives HiD-Net, a second-order (high-order neighbor-aware) graph diffusion network motivated by label monophily.
Problem
Existing diffusion-based GNNs lack a common diffusion framework that formally unifies them, and first-order diffusion assumes homophily among 1-hop neighbors, which fails on heterophily graphs and under noisy edges or features.
Approach
A general diffusion equation with a fidelity term (pull toward initial features) plus a divergence of diffusion flux, shown to recover several GNNs as special cases; HiD-Net adds a 2-hop regularized diffusion term motivated by the monophily property of labels, yielding a second-order random-walk-like propagation.
Key results
- HiD-Net reports the best results on all seven datasets in the node classification table, e.g., Chameleon F1-macro 61.0 vs. 58.0 for DGC and Squirrel F1-macro 47.5 vs. 42.1 for DGC.
- On Cora, HiD-Net reaches 82.8 F1-macro and 84.0 F1-micro, versus 82.2 and 83.2 for APPNP.
- On ogbn-arxiv, HiD-Net reports 72.2 accuracy versus 71.9 for GRAND++.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use HiD-Net instead of APPNP | node classification · Cora | F1-macro: 82.2 -> 82.8 | Helped |
| Use HiD-Net instead of DGC | node classification · Citeseer | F1-micro: 72.5 -> 73.2 | Helped |
| Use HiD-Net instead of APPNP | node classification · Pubmed | F1-micro: 79.9 -> 81.1 | Helped |
| Use HiD-Net instead of DGC | node classification · Chameleon | F1-macro: 58.0 -> 61.0 | Helped |
| Use HiD-Net instead of DGC | node classification · Squirrel | F1-macro: 42.1 -> 47.5 | Helped |
| Use HiD-Net instead of DGC | node classification · Actor | F1-macro: 31.6 -> 25.7 | Hurt |
| Use HiD-Net instead of GRAND++ | node classification · ogbn-arxiv | Accuracy: 71.9 -> 72.2 | Helped |
| Increase alpha from 0 to 1 (ablation) | HiD-Net · citation graphs; Chameleon; Squirrel; Actor | accuracy | Mixed |
| Increase beta from 0 to 1 (ablation) | HiD-Net · all datasets | accuracy | Helped |
| Increase gamma from 0 to 0.6 (ablation) | HiD-Net · all datasets | accuracy | No clear effect |
| Increase gamma from 0 to 0.6 (ablation) | HiD-Net · Cora and Chameleon | accuracy | Mixed |
Surprising findings
- On Actor, DGC (31.6 F1-macro) outperforms HiD-Net (25.7 F1-macro), contrary to the claim of overall superiority.
Limitations
- Diffusivity coefficient is constant; time- and space-dependent learnable diffusivity is left for future work.
- HiD-Net does not outperform DGC on Actor in F1-macro and AUC is less favorable there, and the framework's unification relies on propositions that adapt existing models under specific parameter choices.
Experimental setup
Datasets: Cora Citeseer Pubmed Chameleon Squirrel Actor ogbn-arxiv
Benchmarks: Cora Citeseer Pubmed Chameleon Squirrel Actor ogbn-arxiv
Metrics: F1-macro F1-micro AUC accuracy
Baselines: GCN GAT APPNP GRAND GRAND++ DGC ADC
Builds on: APPNP GRAND DGC ADC Graph Heat Equation
Closest papers by meaning
- Diffusing to the Top: Boost Graph Neural Networks with Minimal Hyperparameter Tuning (ICLR 2025 · similarity 0.90)
- Faster Local Solvers for Graph Diffusion Equations (NeurIPS 2024 · similarity 0.89)
- Towards a Mechanistic Explanation of Diffusion Model Generalization (ICML 2025 · similarity 0.88)
- Learning to Approximate Adaptive Kernel Convolution on Graphs (AAAI 2024 · similarity 0.88)
- Feature Transportation Improves Graph Neural Networks (AAAI 2024 · similarity 0.88)
- On the Interplay between Graph Structure and Learning Algorithms in Graph Neural Networks (ICML 2025 · similarity 0.88)
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