Hypergraph Generation via Structured Stochastic Diffusion

• URL: http://arxiv.org/abs/2605.05024v1
• Date: Wed, 06 May 2026 15:19:20 GMT
• Title: Hypergraph Generation via Structured Stochastic Diffusion
• Abstract summary: HEDGE is a generative model defined directly on relaxed incidence matrices.<n> conditional means, scores, and reverse-drift targets are available in closed form.<n>We show improved hypergraph generation quality relative to strong baselines.
• Score: 8.501793261157966
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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