# HYGENE: A Diffusion-based Hypergraph Generation Method

arXiv: https://arxiv.org/abs/2408.16457 · HTML: https://mlsanity.com/paper/2408.16457/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 46 references that are in the map.
- First posted on arXiv 29 Aug 2024.

## Builds on (most cited first, 25 of 25)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Sign and Basis Invariant Networks for Spectral Graph Representation Learning](https://mlsanity.com/paper/2202.13013/) (2022)
- [SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators](https://mlsanity.com/paper/2204.01613/) (2022)
- [Autoregressive Diffusion Model for Graph Generation](https://mlsanity.com/paper/2307.08849/) (2023)
- [Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modeling](https://mlsanity.com/paper/2305.04111/) (2023)
- [A Survey on Deep Graph Generation: Methods and Applications](https://mlsanity.com/paper/2203.06714/) (2022)
- [Molecular Hypergraph Grammar with its Application to Molecular Optimization](https://mlsanity.com/paper/1809.02745/) (2018)
- [Efficient and Scalable Graph Generation through Iterative Local Expansion](https://mlsanity.com/paper/2312.11529/) (2023)
- [Structural Patterns and Generative Models of Real-world Hypergraphs](https://mlsanity.com/paper/2006.07060/) (2020)
- [Stochastic Block Model for Hypergraphs: Statistical limits and a semidefinite programming approach](https://mlsanity.com/paper/1807.02884/) (2018)
- [Hypernetwork Science via High-Order Hypergraph Walks](https://mlsanity.com/paper/1906.11295/) (2019)
- [Construction and Random Generation of Hypergraphs with Prescribed Degree and Dimension Sequences](https://mlsanity.com/paper/2004.05429/) (2020)
- [DE-HNN: An effective neural model for Circuit Netlist representation](https://mlsanity.com/paper/2404.00477/) (2024)
- [Epidemics on Hypergraphs: Spectral Thresholds for Extinction](https://mlsanity.com/paper/2103.07319/) (2021)
- [Hypergraph Ego-networks and Their Temporal Evolution](https://mlsanity.com/paper/2112.03498/) (2021)
- [MolHF: A Hierarchical Normalizing Flow for Molecular Graph Generation](https://mlsanity.com/paper/2305.08457/) (2023)
- [Generative Hypergraph Models and Spectral Embedding](https://mlsanity.com/paper/2207.13895/) (2022)
- [An Unpooling Layer for Graph Generation](https://mlsanity.com/paper/2206.01874/) (2022)

## Built on by (most cited first, 9 of 9)

- [HOG-Diff: Higher-Order Guided Diffusion for Graph Generation](https://mlsanity.com/paper/2502.04308/) (2025)
- [Recent Advances in Hypergraph Neural Networks](https://mlsanity.com/paper/2503.07959/) (2025)
- [Hypergraph Neural Diffusion: A PDE-Inspired Framework for Hypergraph Message Passing](https://mlsanity.com/paper/2604.10955/) (2026)
- [Variational Graph Contrastive Learning](https://mlsanity.com/paper/2411.07150/) (2024)
- [Feature-Aware (Hyper)graph Generation via Next-Scale Prediction](https://mlsanity.com/paper/2506.01467/) (2025)
- [ArtNet: Hierarchical Clustering-Based Artificial Netlist Generator for ML and DTCO Application](https://mlsanity.com/paper/2510.13582/) (2025)
- [Hypergraph Generation via Structured Stochastic Diffusion](https://mlsanity.com/paper/2605.05024/) (2026)
- [HYVINT: Intensity-Driven Hypergraph Generation with Variational Embeddings](https://mlsanity.com/paper/2605.16836/) (2026)
- [Structural-Functional Brain Connectivity Generation via Multimodal Hypergraph-based Flow Matching](https://mlsanity.com/paper/2610.02722/) (2026)

## Abstract (arXiv)

Hypergraphs are powerful mathematical structures that can model complex, high-order relationships in various domains, including social networks, bioinformatics, and recommender systems. However, generating realistic and diverse hypergraphs remains challenging due to their inherent complexity and lack of effective generative models. In this paper, we introduce a diffusion-based Hypergraph Generation (HYGENE) method that addresses these challenges through a progressive local expansion approach. HYGENE works on the bipartite representation of hypergraphs, starting with a single pair of connected nodes and iteratively expanding it to form the target hypergraph. At each step, nodes and hyperedges are added in a localized manner using a denoising diffusion process, which allows for the construction of the global structure before refining local details. Our experiments demonstrated the effectiveness of HYGENE, proving its ability to closely mimic a variety of properties in hypergraphs. To the best of our knowledge, this is the first attempt to employ deep learning models for hypergraph generation, and our work aims to lay the groundwork for future research in this area.