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Hypergraph Generation via Structured Stochastic Diffusion
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Proposes HEDGE, a structured heat–OU stochastic diffusion on relaxed hypergraph incidence matrices, trained by regressing a state-only reverse-drift network onto exact conditional targets, and shows improved hypergraph generation on six real datasets.
Problem
Generating realistic hypergraphs, where node participation, hyperedge-size heterogeneity and overlap structure must be captured without pairwise reduction.
Approach
A forward diffusion in incidence space that combines a two-sided hypergraph heat operator (node-side and hyperedge-side normalised Laplacians) near the data with an Ornstein–Uhlenbeck component late in time, making the conditional forward process linear-Gaussian so exact reverse-drift targets are available for regression.
Key results
- Full HEDGE achieves the best Intersection WD on all six real datasets, per the paper's comparison against HCM-MCMC, ER-HG and HYGENE.
- HEDGE gives the best Overlap Tail Gap on five of six datasets and ties HCM-MCMC on CiteSeer.
- In simulated ablations, full HEDGE is best on all five reported metrics (e.g., Intersection WD 0.105 vs 0.132 for OU only).
Surprising findings
- Configuration-style HCM-MCMC remains highly competitive on degree and hyperedge-size marginals, which the authors attribute to it directly targeting those quantities.
Limitations
- Evaluation uses fixed-size subhypergraphs rather than fully variable-size generation.
- Generates unweighted, unattributed incidence matrices only.
- Final thresholding projection does not enforce constraints such as non-empty hyperedges or no isolated nodes; spectral operators may need approximation for larger hypergraphs.
Experimental setup
Datasets: Cora CiteSeer Actor House-Committees DBLP Twitch
Benchmarks: Cora CiteSeer Actor House-Committees DBLP Twitch
Metrics: Overlap Tail Gap Intersection WD Feature MMD Node spectral WD Edge spectral WD
Baselines: HCM-MCMC ER-HG HYGENE
Builds on: score-based diffusion (Anderson time reversal) HYGENE normalised hypergraph Laplacian
Closest papers by meaning
- HYGENE: A Diffusion-Based Hypergraph Generation Method (AAAI 2025 · similarity 0.89)
- Pard: Permutation-Invariant Autoregressive Diffusion for Graph Generation (NeurIPS 2024 · similarity 0.87)
- Discrete-state Continuous-time Diffusion for Graph Generation (NeurIPS 2024 · similarity 0.87)
- DiPhon: Diffusion on Graphons for Scalable Graph Generation (NeurIPS 2026 · similarity 0.87)
- SBGD: Improving Graph Diffusion Generative Model via Stochastic Block Diffusion (ICML 2025 · similarity 0.86)
- How Particle System Theory Enhances Hypergraph Message Passing (NeurIPS 2025 · similarity 0.86)
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