# Hyperbolic Geometric Latent Diffusion Model for Graph Generation

arXiv: https://arxiv.org/abs/2405.03188 · HTML: https://mlsanity.com/paper/2405.03188/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 30 of its 48 references that are in the map.
- First posted on arXiv 6 May 2024.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 30)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [GraphGAN: Graph Representation Learning with Generative Adversarial Nets](https://mlsanity.com/paper/1711.08267/) (2017)
- [Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoders](https://mlsanity.com/paper/1901.06033/) (2019)
- [Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modeling](https://mlsanity.com/paper/2305.04111/) (2023)
- [Constrained Generation of Semantically Valid Graphs via Regularizing Variational Autoencoders](https://mlsanity.com/paper/1809.02630/) (2018)
- [Spherical Latent Spaces for Stable Variational Autoencoders](https://mlsanity.com/paper/1808.10805/) (2018)
- [Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs](https://mlsanity.com/paper/2104.02228/) (2021)
- [GraphGDP: Generative Diffusion Processes for Permutation Invariant Graph Generation](https://mlsanity.com/paper/2212.01842/) (2022)
- [A Survey on Graph Diffusion Models: Generative AI in Science for Molecule, Protein and Material](https://mlsanity.com/paper/2304.01565/) (2023)
- [A Self-supervised Mixed-curvature Graph Neural Network](https://mlsanity.com/paper/2112.05393/) (2021)
- [Adversarial Network Embedding](https://mlsanity.com/paper/1711.07838/) (2017)
- [Motif-aware Riemannian Graph Neural Network with Generative-Contrastive Learning](https://mlsanity.com/paper/2401.01232/) (2024)
- [Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learning](https://mlsanity.com/paper/2305.18962/) (2023)
- [Directional diffusion models for graph representation learning](https://mlsanity.com/paper/2306.13210/) (2023)
- [Adversarial Autoencoders with Constant-Curvature Latent Manifolds](https://mlsanity.com/paper/1812.04314/) (2018)
- [A nonuniform popularity-similarity optimization (nPSO) model to efficiently generate realistic complex networks with communities](https://mlsanity.com/paper/1707.07325/) (2017)
- [A Wrapped Normal Distribution on Hyperbolic Space for Gradient-Based Learning](https://mlsanity.com/paper/1902.02992/) (2019)

## Built on by (most cited first, 20 of 20)

- [Hyperbolic Fine-Tuning for Large Language Models](https://mlsanity.com/paper/2410.04010/) (2024)
- [Hyperbolic Deep Learning for Foundation Models: A Survey](https://mlsanity.com/paper/2507.17787/) (2025)
- [Hyperbolic Diffusion Recommender Model](https://mlsanity.com/paper/2504.01541/) (2025)
- [HOG-Diff: Higher-Order Guided Diffusion for Graph Generation](https://mlsanity.com/paper/2502.04308/) (2025)
- [HC-GLAD: Dual Hyperbolic Contrastive Learning for Unsupervised Graph-Level Anomaly Detection](https://mlsanity.com/paper/2407.02057/) (2024)
- [Klein Model for Hyperbolic Neural Networks](https://mlsanity.com/paper/2410.16813/) (2024)
- [Hyperbolic Busemann Neural Networks](https://mlsanity.com/paper/2602.18858/) (2026)
- [Principled Latent Diffusion for Graphs via Laplacian Autoencoders](https://mlsanity.com/paper/2601.13780/) (2026)
- [GGBall: Graph Generative Model on Poincar'e Ball](https://mlsanity.com/paper/2506.07198/) (2025)
- [Modality Alignment across Trees on Heterogeneous Hyperbolic Manifolds](https://mlsanity.com/paper/2510.27391/) (2025)
- [Satellites Reveal Mobility: A Commuting Origin-destination Flow Generator for Global Cities](https://mlsanity.com/paper/2505.15870/) (2025)
- [An Out-Of-Distribution Membership Inference Attack Approach for Cross-Domain Graph Attacks](https://mlsanity.com/paper/2505.20074/) (2025)
- [Toward a Unified Geometry Understanding: Riemannian Diffusion Framework for Graph Generation and Prediction](https://mlsanity.com/paper/2510.04522/) (2025)
- [Towards LLM-Empowered Knowledge Tracing via LLM-Student Hierarchical Behavior Alignment in Hyperbolic Space](https://mlsanity.com/paper/2602.22879/) (2026)
- [Cross-Cultural Fashion Design via Interactive Large Language Models and Diffusion Models](https://mlsanity.com/paper/2501.15571/) (2025)
- [BadGraph: A Backdoor Attack Against Latent Diffusion Model for Text-Guided Graph Generation](https://mlsanity.com/paper/2510.20792/) (2025)
- [Forget Less by Learning from Parents Through Hierarchical Relationships](https://mlsanity.com/paper/2601.01892/) (2026)
- [Hierarchy-Guided Topology Latent Flow for Molecular Graph Generation](https://mlsanity.com/paper/2603.27113/) (2026)
- [Learning Taxonomic Trees with Hierarchical Representation Regularization for Large Multimodal Models](https://mlsanity.com/paper/2607.02909/) (2026)
- [GeoGAE: Scalable Graph-Level Autoencoding via Hyperball Cloud Representations](https://mlsanity.com/paper/2609.35527/) (2026)

## Abstract (arXiv)

Diffusion models have made significant contributions to computer vision, sparking a growing interest in the community recently regarding the application of them to graph generation. Existing discrete graph diffusion models exhibit heightened computational complexity and diminished training efficiency. A preferable and natural way is to directly diffuse the graph within the latent space. However, due to the non-Euclidean structure of graphs is not isotropic in the latent space, the existing latent diffusion models effectively make it difficult to capture and preserve the topological information of graphs. To address the above challenges, we propose a novel geometrically latent diffusion framework HypDiff. Specifically, we first establish a geometrically latent space with interpretability measures based on hyperbolic geometry, to define anisotropic latent diffusion processes for graphs. Then, we propose a geometrically latent diffusion process that is constrained by both radial and angular geometric properties, thereby ensuring the preservation of the original topological properties in the generative graphs. Extensive experimental results demonstrate the superior effectiveness of HypDiff for graph generation with various topologies.