Hypergraph Generation via Structured Stochastic Diffusion

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• arXiv

Abstract

Hypergraphs model higher-order interactions, but realistic hypergraph generation remains difficult because incidence, hyperedge-size heterogeneity, and overlap structure are not faithfully captured by pairwise reductions. We propose HEDGE, a generative model defined directly on relaxed incidence matrices via a structured stochastic diffusion. The forward process combines a hypergraph-specific two-sided heat operator with an Ornstein–Uhlenbeck component, preserving structure-aware noising near the data while yielding an explicit Gaussian terminal law. Conditional on an observed hypergraph, this forward process is linear-Gaussian, so conditional means, covariances, scores, and reverse-drift targets are available in closed form. We therefore learn a permutation-equivariant state-only reverse-drift field in incidence space by regressing onto exact conditional targets, and generate samples by simulating a learned reverse-time SDE from the Gaussian base law. We establish exactness in the ideal state-only setting together with finite-horizon stability guarantees, and empirically show improved hypergraph generation quality relative to strong baselines.

Citation

Nemeth, C. (2026). Hypergraph Generation via Structured Stochastic Diffusion. arXiv preprint.

@article{nemeth2026hypergraph,
  title={Hypergraph Generation via Structured Stochastic Diffusion},
  author={Nemeth, Christopher},
  journal={arXiv preprint arXiv:2605.05024},
  year={2026}
}