mlsanityData to 14 Oct 2026

From topology learning to graph generation: A unifying perspective

arXiv 2609.02286 ↗First posted 2 Sep 2026stat.ML cs.LG eess.SPcited by 0

Not on the map. Why?

Abstract (arXiv)

Learning graph structures from data is a fundamental problem that spans a wide range of signal processing and machine learning tasks. While significant effort has been made to tackle the problem, existing research has largely evolved along two parallel directions. The first seeks to infer the topology of an individual graph from observations supported on it, whereas the second seeks to learn a generative distribution from observed graph instances, enabling the sampling of new graphs. This review presents a unified framework that connects these formulations by viewing them as inverse problems of a common generation process for graph data. We review the major methodologies within this framework, highlight their relationships, strengths, and limitations, and identify opportunities for integrating ideas across paradigms. By bridging graph topology learning and graph generation, this review provides a broader cross-disciplinary perspective on the field and outlines promising directions for future research.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 135 of its 189 references that are in the map. First posted on arXiv 2 Sep 2026.

Builds on

135 of 189 references.

References · 135

  1. 2022Flow Matching for Generative Modelingcited by 5,702
  2. 2013Auto-Encoding Variational Bayescited by 4,053
  3. 2016Variational Graph Auto-Encoderscited by 1,382
  4. 2020Learning to Simulate Complex Physics with Graph Networkscited by 880
  5. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 752
  6. 2018Junction Tree Variational Autoencoder for Molecular Graph Generationcited by 652
  7. 2022DiGress: Discrete Denoising diffusion for graph generationcited by 520
  8. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 516
  9. 2018GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Modelscited by 413
  10. 2018MolGAN: An implicit generative model for small molecular graphscited by 393
  11. 2018GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoderscited by 383
  12. 2020Graph Structure Learning for Robust Graph Neural Networkscited by 371
38 more
  1. 2018Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generationcited by 364
  2. 2018Neural Relational Inference for Interacting Systemscited by 339
  3. 2019DAG-GNN: DAG Structure Learning with Graph Neural Networkscited by 331
  4. 2020GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generationcited by 305
  5. 2024Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Designcited by 305
  6. 2022Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equationscited by 283
  7. 2020Permutation Invariant Graph Generation via Score-Based Generative Modelingcited by 270
  8. 2018Approximation Methods for Bilevel Programmingcited by 236
  9. 2019Efficient Graph Generation with Graph Recurrent Attention Networkscited by 234
  10. 2019Learning Discrete Structures for Graph Neural Networkscited by 231
  11. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 214
  12. 2019Learning Sparse Nonparametric DAGscited by 207
  13. 2020DYNOTEARS: Structure Learning from Time-Series Datacited by 200
  14. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 191
  15. 2021GraphDF: A Discrete Flow Model for Molecular Graph Generationcited by 180
  16. 2022Bayesian Structure Learning with Generative Flow Networkscited by 153
  17. 2016How to learn a graph from smooth signalscited by 146
  18. 2018NetGAN: Generating Graphs via Random Walkscited by 131
  19. 2018Learning graphs from data: A signal representation perspectivecited by 119
  20. 2019GraphNVP: An Invertible Flow Model for Generating Molecular Graphscited by 116
  21. 2018Connecting the Dots: Identifying Network Structure via Graph Signal Processingcited by 111
  22. 2020Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Datacited by 100
  23. 2023A Fully First-Order Method for Stochastic Bilevel Optimizationcited by 100
  24. 2022SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generatorscited by 99
  25. 2020A Systematic Survey on Deep Generative Models for Graph Generationcited by 94
  26. 2018Bayesian graph convolutional neural networks for semi-supervised classificationcited by 89
  27. 2020Differentiable Graph Module (DGM) for Graph Convolutional Networkscited by 86
  28. 2024Variational Flow Matching for Graph Generationcited by 83
  29. 2024DeFoG: Discrete Flow Matching for Graph Generationcited by 82
  30. 2024Discrete-state Continuous-time Diffusion for Graph Generationcited by 76
  31. 2025The Principles of Diffusion Modelscited by 76
  32. 2022Diffusion Models for Graphs Benefit From Discrete State Spacescited by 73
  33. 2021A Survey on Graph Structure Learning: Progress and Opportunitiescited by 71
  34. 2022A Survey on Deep Graph Generation: Methods and Applicationscited by 69
  35. 2022Learning to Induce Causal Structurecited by 68
  36. 2016Network Topology Inference from Spectral Templatescited by 58
  37. 2017Network Inference via the Time-Varying Graphical Lassocited by 55
  38. 2023Graph Generation with Diffusion Mixturecited by 55

50 most cited of 135 All 135 (JSON)

Built on by

Not cited yet.