# Hypergraph Generation via Structured Stochastic Diffusion

arXiv: https://arxiv.org/abs/2605.05024 · HTML: https://mlsanity.com/paper/2605.05024/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 45 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 24 of 24)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators](https://mlsanity.com/paper/2204.01613/) (2022)
- [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018)
- [Generator Matching: Generative modeling with arbitrary Markov processes](https://mlsanity.com/paper/2410.20587/) (2024)
- [DeFoG: Discrete Flow Matching for Graph Generation](https://mlsanity.com/paper/2410.04263/) (2024)
- [Generative hypergraph clustering: from blockmodels to modularity](https://mlsanity.com/paper/2101.09611/) (2021)
- [Structural Patterns and Generative Models of Real-world Hypergraphs](https://mlsanity.com/paper/2006.07060/) (2020)
- [Consistency of Spectral Hypergraph Partitioning under Planted Partition Model](https://mlsanity.com/paper/1505.01582/) (2015)
- [Transport Elliptical Slice Sampling](https://mlsanity.com/paper/2210.10644/) (2022)
- [Tuning-Free Maximum Likelihood Training of Latent Variable Models via Coin Betting](https://mlsanity.com/paper/2305.14916/) (2023)
- [HYGENE: A Diffusion-based Hypergraph Generation Method](https://mlsanity.com/paper/2408.16457/) (2024)
- [Latent Space Modelling of Hypergraph Data](https://mlsanity.com/paper/1909.00472/) (2019)
- [SwISS: A Scalable Markov chain Monte Carlo Divide-and-Conquer Strategy](https://mlsanity.com/paper/2208.04080/) (2022)
- [DHG-Bench: A Comprehensive Benchmark for Deep Hypergraph Learning](https://mlsanity.com/paper/2508.12244/) (2025)
- [Gaussian Processes on Hypergraphs](https://mlsanity.com/paper/2106.01982/) (2021)
- [Finding Bipartite Components in Hypergraphs](https://mlsanity.com/paper/2205.02771/) (2022)
- [Denoising Diffused Embeddings: a Generative Approach for Hypergraphs](https://mlsanity.com/paper/2501.01541/) (2025)
- [Generator-based Graph Generation via Heat Diffusion](https://mlsanity.com/paper/2602.03612/) (2026)

## Abstract (arXiv)

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.