mlsanityData to 13 Oct 2026

Discrete-state Continuous-time Diffusion for Graph Generation

arXiv 2405.11416 ↗First posted 19 May 2024cs.LGcited by 75

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

Abstract (arXiv)

Graph is a prevalent discrete data structure, whose generation has wide applications such as drug discovery and circuit design. Diffusion generative models, as an emerging research focus, have been applied to graph generation tasks. Overall, according to the space of states and time steps, diffusion generative models can be categorized into discrete-/continuous-state discrete-/continuous-time fashions. In this paper, we formulate the graph diffusion generation in a discrete-state continuous-time setting, which has never been studied in previous graph diffusion models. The rationale of such a formulation is to preserve the discrete nature of graph-structured data and meanwhile provide flexible sampling trade-offs between sample quality and efficiency. Analysis shows that our training objective is closely related to generation quality, and our proposed generation framework enjoys ideal invariant/equivariant properties concerning the permutation of node ordering. Our proposed model shows competitive empirical performance against state-of-the-art graph generation solutions on various benchmarks and, at the same time, can flexibly trade off the generation quality and efficiency in the sampling phase.

Key facts. Cited by 75 papers in the map (data through 13 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 59 of its 87 references that are in the map. First posted on arXiv 19 May 2024.

Builds on

59 of 87 references.

Closest ancestors · 12

Same direction, newest first

  1. 2023Autoregressive Diffusion Model for Graph Generation17 Jul
  2. 2023Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modeling6 May
  3. 2023Geometric Latent Diffusion Models for 3D Molecule Generation2 May
  4. 2023Data-Centric Learning from Unlabeled Graphs with Diffusion Model17 Mar
  5. 2023Generative Diffusion Models on Graphs: Methods and Applications6 Feb
  6. 2022Diffusion Models for Graphs Benefit From Discrete State Spaces4 Oct
  7. 2022DiGress: Discrete Denoising diffusion for graph generation29 Sep
  8. 2022MDM: Molecular Diffusion Model for 3D Molecule Generation13 Sep
  9. 2022Equivariant Diffusion for Molecule Generation in 3D31 Mar
  10. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation6 Mar
  11. 2022Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations5 Feb
  12. 2020Permutation Invariant Graph Generation via Score-Based Generative Modeling2 Mar

Other references · 47

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,952
  2. 2020Denoising Diffusion Implicit Modelscited by 9,718
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,028
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,023
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,077
  6. 2017Neural Message Passing for Quantum Chemistrycited by 3,471
  7. 2017FiLM: Visual Reasoning with a General Conditioning Layercited by 2,306
  8. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,685
  9. 2021Variational Diffusion Modelscited by 1,148
  10. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,112
  11. 2016Automatic chemical design using a data-driven continuous representation of moleculescited by 764
  12. 2018Junction Tree Variational Autoencoder for Molecular Graph Generationcited by 648
35 more
  1. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 570
  2. 2020Principal Neighbourhood Aggregation for Graph Netscited by 478
  3. 2022A Continuous Time Framework for Discrete Denoising Modelscited by 442
  4. 2018GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Modelscited by 410
  5. 2018MolGAN: An implicit generative model for small molecular graphscited by 392
  6. 2018GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoderscited by 378
  7. 2018GuacaMol: Benchmarking Models for De Novo Molecular Designcited by 295
  8. 2023Understanding Diffusion Objectives as the ELBO with Simple Data Augmentationcited by 294
  9. 2018Molecular Sets (MOSES): A Benchmarking Platform for Molecular Generation Modelscited by 271
  10. 2022Torsional Diffusion for Molecular Conformer Generationcited by 262
  11. 2020Can Graph Neural Networks Count Substructures?cited by 235
  12. 2019Efficient Graph Generation with Graph Recurrent Attention Networkscited by 233
  13. 2021Identity-aware Graph Neural Networkscited by 197
  14. 2022Pure Transformers are Powerful Graph Learnerscited by 188
  15. 2022Score-based Continuous-time Discrete Diffusion Modelscited by 169
  16. 2021Learning Gradient Fields for Molecular Conformation Generationcited by 162
  17. 2022Data Augmentation for Deep Graph Learning: A Surveycited by 133
  18. 2019GraphNVP: An Invertible Flow Model for Generating Molecular Graphscited by 115
  19. 2022Transformer for Graphs: An Overview from Architecture Perspectivecited by 107
  20. 2022SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generatorscited by 98
  21. 2022Exploring Chemical Space with Score-based Out-of-distribution Generationcited by 95
  22. 2022Equivariant Energy-Guided SDE for Inverse Molecular Designcited by 73
  23. 2023On the Connection Between MPNN and Graph Transformercited by 61
  24. 2022DiffBP: Generative Diffusion of 3D Molecules for Target Protein Bindingcited by 58
  25. 2016GANS for Sequences of Discrete Elements with the Gumbel-softmax Distributioncited by 47
  26. 2022GraphGDP: Generative Diffusion Processes for Permutation Invariant Graph Generationcited by 43
  27. 2021Top-N: Equivariant set and graph generation without exchangeabilitycited by 36
  28. 2023Networked Time Series Imputation via Position-aware Graph Enhanced Variational Autoencoderscited by 32
  29. 2023Class-Imbalanced Graph Learning without Class Rebalancingcited by 29
  30. 2021Graph Sanitation with Application to Node Classificationcited by 20
  31. 2023Graph Neural Banditscited by 20
  32. 2021A Graph VAE and Graph Transformer Approach to Generating Molecular Graphscited by 16
  33. 2023Reconstructing Graph Diffusion History from a Single Snapshotcited by 13
  34. 2023FairGen: Towards Fair Graph Generationcited by 12
  35. 2023Neural Contextual Bandits for Personalized Recommendationcited by 10

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2024: 7; 2025: 39; 2026: 29.

75 papers.

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  1. 2026Categorical Flow Mapscited by 42
  2. 2024How Efficient is LLM-Generated Code? A Rigorous & High-Standard Benchmarkcited by 40
  3. 2024Cometh: A continuous-time discrete-state graph diffusion modelcited by 30
  4. 2025MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Controlcited by 20
  5. 2025Diffuse Everything: Multimodal Diffusion Models on Arbitrary State Spacescited by 19
  6. 2025SelfElicit: Your Language Model Secretly Knows Where is the Relevant Evidencecited by 18
  7. 2025Pave Your Own Path: Graph Gradual Domain Adaptation on Fused Gromov-Wasserstein Geodesicscited by 17
  8. 2025Graph Generative Pre-trained Transformercited by 16
  9. 2024Can Graph Neural Networks Learn Language with Extremely Weak Text Supervision?cited by 13
  10. 2024Gradient Compressed Sensing: A Query-Efficient Gradient Estimator for High-Dimensional Zeroth-Order Optimizationcited by 12
  11. 2025Flatten Graphs as Sequences: Transformers are Scalable Graph Generatorscited by 12
  12. 2025Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecastingcited by 12
38 more
  1. 2025Dynamic Generation of Multi-LLM Agents Communication Topologies with Graph Diffusion Modelscited by 11
  2. 2024Ask, and it shall be given: On the Turing completeness of promptingcited by 10
  3. 2024Improving Molecular Graph Generation with Flow Matching and Optimal Transportcited by 10
  4. 2025PLANETALIGN: A Comprehensive Python Library for Benchmarking Network Alignmentcited by 10
  5. 2025Hierarchical LoRA MoE for Efficient CTR Model Scalingcited by 10
  6. 2025Simple and Critical Iterative Denoising: A Recasting of Discrete Diffusion in Graph Generationcited by 9
  7. 2026Prune as You Generate: Online Rollout Pruning for Faster and Better RLVRcited by 9
  8. 2024InterFormer: Effective Heterogeneous Interaction Learning for Click-Through Rate Predictioncited by 8
  9. 2025HOG-Diff: Higher-Order Guided Diffusion for Graph Generationcited by 7
  10. 2025Graph Data Selection for Domain Adaptation: A Model-Free Approachcited by 7
  11. 2025Bures-Wasserstein Flow Matching for Graph Generationcited by 7
  12. 2025Learning Flexible Forward Trajectories for Masked Molecular Diffusioncited by 6
  13. 2025FragFM: Hierarchical Framework for Efficient Molecule Generation via Fragment-Level Discrete Flow Matchingcited by 5
  14. 2025PowerGrow: Feasible Co-Growth of Structures and Dynamics for Power Grid Synthesiscited by 5
  15. 2025Backdoor Attacks on Discrete Graph Diffusion Modelscited by 3
  16. 2025Recent Developments in GNNs for Drug Discoverycited by 3
  17. 2025GGBall: Graph Generative Model on Poincar'e Ballcited by 3
  18. 2025Generating Directed Graphs with Dual Attention and Asymmetric Encodingcited by 3
  19. 2025Continuous-time Discrete-space Diffusion Model for Recommendationcited by 3
  20. 2026Principled Latent Diffusion for Graphs via Laplacian Autoencoderscited by 3
  21. 2026Graph-GRPO: Training Graph Flow Models with Reinforcement Learningcited by 3
  22. 2025A Diffusive Data Augmentation Framework for Reconstruction of Complex Network Evolutionary Historycited by 2
  23. 2025Fast Graph Generation via Autoregressive Noisy Filtration Modelingcited by 2
  24. 2025Composable Score-based Graph Diffusion Model for Multi-Conditional Molecular Generationcited by 2
  25. 2025Continual Low-Rank Adapters for LLM-based Generative Recommender Systemscited by 2
  26. 2026Flowette: Flow Matching with Graphette Priors for Graph Generationcited by 2
  27. 2026Unrestrained Simplex Denoising for Discrete Data. A Non-Markovian Approach Applied to Graph Generationcited by 2
  28. 2026Learning Discrete Diffusion of Graphs via Free-Energy Gradient Flowscited by 2
  29. 2025DMol: A Highly Efficient and Chemical Motif-Preserving Molecule Generation Platformcited by 1
  30. 2025Saffron-1: Safety Inference Scalingcited by 1
  31. 2025Decoding Cortical Microcircuits: A Generative Model for Latent Space Exploration and Controlled Synthesiscited by 1
  32. 2025Graph Homophily Booster: Rethinking the Role of Discrete Features on Heterophilic Graphscited by 1
  33. 2025Transport-Coupled Bayesian Flows for Molecular Graph Generationcited by 1
  34. 2026Variational Bayesian Flow Network for Graph Generationcited by 1
  35. 2026Graph homophily booster: Reimagining the role of discrete features in heterophilic graph learningcited by 1
  36. 2026ReMix: Reinforcement routing for mixtures of LoRAs in LLM finetuningcited by 1
  37. 2026Hierarchical Discrete Flow Matching for Graph Generationcited by 1
  38. 2026AvAtar: Learning to Align via Active Optimal Transportcited by 1

50 most cited of 75 All 75 (JSON)

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  1. 2024Diffusion-based Graph Generative Methods
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  3. 2024Advancing Graph Generation through Beta Diffusion
  4. 2022Fast Graph Generation via Spectral Diffusion
  5. 2023Complex Preferences for Different Convergent Priors in Discrete Graph Diffusion
  6. 2024Generative Modelling of Structurally Constrained Graphs
  7. 2023Conditional Diffusion Based on Discrete Graph Structures for Molecular Graph Generation
  8. 2023A Survey on Graph Diffusion Models: Generative AI in Science for Molecule, Protein and Material