mlsanityData to 14 Oct 2026

Hyperbolic Geometric Latent Diffusion Model for Graph Generation

arXiv 2405.03188 ↗First posted 6 May 2024cs.LGcited by 20

On the map: Diffusion models → Flow matching, time series and science

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.

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.

Builds on

30 of 48 references.

Closest ancestors · 7

Same direction, newest first

  1. 2023Directional diffusion models for graph representation learning22 Jun
  2. 2023Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modeling6 May
  3. 2023Geometric Latent Diffusion Models for 3D Molecule Generation2 May
  4. 2023A Survey on Graph Diffusion Models: Generative AI in Science for Molecule, Protein and Material4 Apr
  5. 2022DiGress: Discrete Denoising diffusion for graph generation29 Sep
  6. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation6 Mar
  7. 2022Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations5 Feb

Other references · 23

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2016Variational Graph Auto-Encoderscited by 1,382
  3. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 684
  4. 2020Reliable Fidelity and Diversity Metrics for Generative Modelscited by 434
  5. 2018GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Modelscited by 413
  6. 2018Hyperbolic Neural Networkscited by 402
  7. 2019Hyperbolic Graph Convolutional Neural Networkscited by 402
  8. 2019Hyperbolic Graph Neural Networkscited by 244
  9. 2018Representation Tradeoffs for Hyperbolic Embeddingscited by 206
  10. 2018Poincar'e GloVe: Hyperbolic Word Embeddingscited by 156
  11. 2017GraphGAN: Graph Representation Learning with Generative Adversarial Netscited by 121
  12. 2019Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoderscited by 112
11 more
  1. 2018Constrained Generation of Semantically Valid Graphs via Regularizing Variational Autoencoderscited by 74
  2. 2018Spherical Latent Spaces for Stable Variational Autoencoderscited by 67
  3. 2021Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphscited by 50
  4. 2022GraphGDP: Generative Diffusion Processes for Permutation Invariant Graph Generationcited by 43
  5. 2021A Self-supervised Mixed-curvature Graph Neural Networkcited by 33
  6. 2017Adversarial Network Embeddingcited by 25
  7. 2024Motif-aware Riemannian Graph Neural Network with Generative-Contrastive Learningcited by 23
  8. 2023Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learningcited by 18
  9. 2018Adversarial Autoencoders with Constant-Curvature Latent Manifoldscited by 12
  10. 2017A nonuniform popularity-similarity optimization (nPSO) model to efficiently generate realistic complex networks with communitiescited by 6
  11. 2019A Wrapped Normal Distribution on Hyperbolic Space for Gradient-Based Learningcited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 3; 2025: 10; 2026: 7.

20 papers.

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  1. 2024Hyperbolic Fine-Tuning for Large Language Modelscited by 27
  2. 2025Hyperbolic Deep Learning for Foundation Models: A Surveycited by 20
  3. 2025Hyperbolic Diffusion Recommender Modelcited by 9
  4. 2025HOG-Diff: Higher-Order Guided Diffusion for Graph Generationcited by 8
  5. 2024HC-GLAD: Dual Hyperbolic Contrastive Learning for Unsupervised Graph-Level Anomaly Detectioncited by 5
  6. 2024Klein Model for Hyperbolic Neural Networkscited by 5
  7. 2026Hyperbolic Busemann Neural Networkscited by 5
  8. 2026Principled Latent Diffusion for Graphs via Laplacian Autoencoderscited by 4
  9. 2025GGBall: Graph Generative Model on Poincar'e Ballcited by 3
  10. 2025Modality Alignment across Trees on Heterogeneous Hyperbolic Manifoldscited by 3
  11. 2025Satellites Reveal Mobility: A Commuting Origin-destination Flow Generator for Global Citiescited by 2
  12. 2025An Out-Of-Distribution Membership Inference Attack Approach for Cross-Domain Graph Attackscited by 2
8 more
  1. 2025Toward a Unified Geometry Understanding: Riemannian Diffusion Framework for Graph Generation and Predictioncited by 2
  2. 2026Towards LLM-Empowered Knowledge Tracing via LLM-Student Hierarchical Behavior Alignment in Hyperbolic Spacecited by 1
  3. 2025Cross-Cultural Fashion Design via Interactive Large Language Models and Diffusion Modelscited by 0
  4. 2025BadGraph: A Backdoor Attack Against Latent Diffusion Model for Text-Guided Graph Generationcited by 0
  5. 2026Forget Less by Learning from Parents Through Hierarchical Relationshipscited by 0
  6. 2026Hierarchy-Guided Topology Latent Flow for Molecular Graph Generationcited by 0
  7. 2026Learning Taxonomic Trees with Hierarchical Representation Regularization for Large Multimodal Modelscited by 0
  8. 2026GeoGAE: Scalable Graph-Level Autoencoding via Hyperball Cloud Representationscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023Hyperbolic Graph Diffusion Model
  2. 2023Graph Generation with Diffusion Mixture
  3. 2026Graph Representation via Elements of Discrete Morse and Cobordism Theories
  4. 2024Diffusion-based Graph Generative Methods
  5. 2022Fast Graph Generation via Spectral Diffusion
  6. 2023Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry
  7. 2025LGDC: Latent Graph Diffusion via Spectrum-Preserving Coarsening
  8. 2023Generative Diffusion Models on Graphs: Methods and Applications