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Hyperbolic Geometric Latent Diffusion Model for Graph Generation
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Proposes HypDiff, a latent diffusion model for graph generation that diffuses hyperbolic node embeddings with radial (popularity) and angular (similarity) geometric constraints.
Problem
Discrete graph diffusion models are computationally expensive, and latent graph diffusion in Euclidean space is ill-suited to the anisotropic, hierarchical structure of graphs, so isotropic noise destroys topological information.
Approach
Two-stage model: a hyperbolic (HGCN) autoencoder followed by a diffusion process in hyperbolic space that adds a radial growth term and angular noise (sign of cluster-center geodesic times Gaussian), applied in tangent planes of h-kmeans cluster centers, with a DDPM-style UNet denoiser predicting x0.
Key results
- On node classification, HypDiff reports average rank 1.1 and Micro-F1 of 82.4 on Cora and 85.7 on Polblogs, ahead of P-VAE and Hype-ANE.
- On graph generation MMD, HypDiff achieves best Degree MMD of 0.002 on Community and best Cluster MMD of 0.004 on PROTEINS, with competitive results versus GraphRNN and EDGE.
- Ablations show removing radial popularity or angular similarity degrades node classification, and the paper reports lower diffusion time and GPU memory than discrete graph diffusion baselines on IMDB-B.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use HypDiff instead of the strongest listed baseline | Node classification · SBM, BA, Cora, Citeseer, and Polblogs | Micro-F1: 57.9±1.3 -> 70.5±0.1 (SBM); 56.9±2.4 -> 58.3±0.1 (BA); 80.7±0.1 -> 82.4±0.1 (Cora); 67.9±1.7 -> 67.8±0.2 (Citeseer); 83. | Helped |
| Use HypDiff instead of the strongest listed baseline | Graph generation · Community, BA-G, MUTAG, and PROTRINS | Degree MMD: 0.002 vs 0.002 (Community); 0.122 -> 0.216 (BA-G); 0.024 -> 0.048 (MUTAG); 0.009 -> 0.133 (PROTRINS) | Mixed |
| Use HypDiff instead of the strongest listed baseline | Graph generation · Community, BA-G, MUTAG, and PROTRINS | Cluster MMD: 0.013 -> 0.010 (Community); 0.010 -> 0.021 (BA-G); 0.013 -> 0.001 (MUTAG); 0.013 -> 0.004 (PROTRINS) | Mixed |
| Use HypDiff instead of the strongest listed baseline | Graph generation · Community, BA-G, MUTAG, and PROTRINS | Spectre MMD: 0.004 -> 0.028 (Community); 0.007 -> 0.004 (BA-G); 0.003 -> 0.040 (MUTAG); 0.013 -> 0.012 (PROTRINS) | Mixed |
| Add radial popularity diffusion constraint (ablation) | HypDiff · Three real-world datasets | node classification performance | Helped |
| Add angular similarity diffusion constraint (ablation) | HypDiff · Three real-world datasets | node classification performance | Helped |
| Add radial popularity and angular similarity geometric priors (ablation) | HypDiff · Three real-world datasets | node classification performance | Helped |
Surprising findings
- GraphRNN obtains the best Degree MMD on several graph generation datasets (e.g., 0.002 on Community, 0.122 on BA-G), outperforming HypDiff on those metrics.
Limitations
- Theoretical claims (non-additivity of wrapped normals, folded-normal limit) are only sketched in appendix, and the angular noise is an approximation using sign functions.
- Sensitivity to cluster count k and radial coefficient delta varies across datasets, requiring tuning.
Experimental setup
Datasets: SBM BA Cora Citeseer Polblogs Community Ego BA-G Grid MUTAG IMDB-B PROTEINS
Benchmarks: Cora Citeseer Polblogs SBM BA Community BA-G MUTAG PROTEINS
Metrics: Micro-F1 Macro-F1 MMD degree MMD clustering MMD spectre F1 pr F1 dc
Baselines: VGAE ANE GraphGAN P-VAE Hype-ANE GraphRNN GDSS DiGress GraphGDP EDGE
Builds on: DDPM Directional Diffusion Model P-VAE HGCN GDSS
Closest papers by meaning
- Hyperbolic Graph Diffusion Model (AAAI 2024 · similarity 0.91)
- Toward a Unified Geometry Understanding : Riemannian Diffusion Framework for Graph Generation and Prediction (NeurIPS 2025 · similarity 0.90)
- Graph Generation with Diffusion Mixture (ICML 2024 · similarity 0.89)
- Generating Graphs via Spectral Diffusion (ICLR 2025 · similarity 0.88)
- Isometric Representation Learning for Disentangled Latent Space of Diffusion Models (ICML 2024 · similarity 0.88)
- TopoDiffusionNet: A Topology-aware Diffusion Model (ICLR 2025 · similarity 0.88)
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