mlsanityData to 7 Oct 2026

Cometh: A continuous-time discrete-state graph diffusion model

arXiv 2406.06449 ↗First posted 10 Jun 2024cs.LGcited by 29

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

Abstract (arXiv)

Discrete-state denoising diffusion models led to state-of-the-art performance in graph generation, especially in the molecular domain. Recently, they have been transposed to continuous time, allowing more flexibility in the reverse process and a better trade-off between sampling efficiency and quality. Here, to leverage the benefits of both approaches, we propose Cometh, a continuous-time discrete-state graph diffusion model, tailored to the specificities of graph data. In addition, we also successfully replaced the set of structural encodings previously used in the discrete graph diffusion model with a single random-walk-based encoding, providing a simple and principled way to boost the model's expressive power. Empirically, we show that integrating continuous time leads to significant improvements across various metrics over state-of-the-art discrete-state diffusion models on a large set of molecular and non-molecular benchmark datasets. In terms of VUN samples, Cometh obtains a near-perfect performance of 99.5% on the planar graph dataset and outperforms DiGress by 12.6% on the large GuacaMol dataset.

Key facts. Cited by 29 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 48 of its 59 references that are in the map. First posted on arXiv 10 Jun 2024.

Builds on

48 of 59 references.

Closest ancestors · 12

Same direction, newest first

  1. 2024Discrete-state Continuous-time Diffusion for Graph Generation19 May
  2. 2024Pard: Permutation-Invariant Autoregressive Diffusion for Graph Generation6 Feb
  3. 2023Sparse Training of Discrete Diffusion Models for Graph Generation3 Nov
  4. 2023Navigating the Design Space of Equivariant Diffusion-Based Generative Models for De Novo 3D Molecule Generation29 Sep
  5. 2023Autoregressive Diffusion Model for Graph Generation17 Jul
  6. 2023Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modeling6 May
  7. 2023MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generation17 Feb
  8. 2022Fast Graph Generation via Spectral Diffusion16 Nov
  9. 2022Diffusion Models for Graphs Benefit From Discrete State Spaces4 Oct
  10. 2022DiGress: Discrete Denoising diffusion for graph generation29 Sep
  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 · 36

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  4. 2022Classifier-Free Diffusion Guidancecited by 5,717
  5. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  6. 2017FiLM: Visual Reasoning with a General Conditioning Layercited by 2,286
  7. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  8. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  9. 2017MoleculeNet: A Benchmark for Molecular Machine Learningcited by 1,037
  10. 2023Discrete Diffusion Modeling by Estimating the Ratios of the Data Distributioncited by 712
  11. 2024Simplified and Generalized Masked Diffusion for Discrete Datacited by 606
  12. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 566
24 more
  1. 2021Rethinking Graph Transformers with Spectral Attentioncited by 468
  2. 2022A Continuous Time Framework for Discrete Denoising Modelscited by 437
  3. 2018GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Modelscited by 406
  4. 2021Graph Neural Networks with Learnable Structural and Positional Representationscited by 326
  5. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
  6. 2020GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generationcited by 301
  7. 2018GuacaMol: Benchmarking Models for De Novo Molecular Designcited by 294
  8. 2018Molecular Sets (MOSES): A Benchmarking Platform for Molecular Generation Modelscited by 270
  9. 2019Efficient Graph Generation with Graph Recurrent Attention Networkscited by 231
  10. 2018Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discoverycited by 191
  11. 2022Sign and Basis Invariant Networks for Spectral Graph Representation Learningcited by 176
  12. 2022Score-based Continuous-time Discrete Diffusion Modelscited by 167
  13. 2023Graph Inductive Biases in Transformers without Message Passingcited by 150
  14. 2022SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generatorscited by 96
  15. 2022HouseDiffusion: Vector Floorplan Generation via a Diffusion Model with Discrete and Continuous Denoisingcited by 72
  16. 2022Improved Vector Quantized Diffusion Modelscited by 62
  17. 2023Graph Generation with Diffusion Mixturecited by 52
  18. 2023MUDiff: Unified Diffusion for Complete Molecule Generationcited by 41
  19. 2023RetroBridge: Modeling Retrosynthesis with Markov Bridgescited by 35
  20. 2023Efficient and Scalable Graph Generation through Iterative Local Expansioncited by 35
  21. 2017On the Combinatorial Power of the Weisfeiler-Lehman Algorithmcited by 18
  22. 2022MGCVAE: Multi-objective Inverse Design via Molecular Graph Conditional Variational Autoencodercited by 16
  23. 2023A Simple and Scalable Representation for Graph Generationcited by 15
  24. 2023Classifier-free graph diffusion for molecular property targetingcited by 13

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 11; 2026: 18.

29 papers.

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  1. 2025Position: Graph Learning Will Lose Relevance Due To Poor Benchmarkscited by 52
  2. 2026Categorical Flow Mapscited by 37
  3. 2025Graph Generative Pre-trained Transformercited by 16
  4. 2025Bures-Wasserstein Flow Matching for Graph Generationcited by 7
  5. 2025HOG-Diff: Higher-Order Guided Diffusion for Graph Generationcited by 6
  6. 2025FragFM: Hierarchical Framework for Efficient Molecule Generation via Fragment-Level Discrete Flow Matchingcited by 5
  7. 2025Generating Directed Graphs with Dual Attention and Asymmetric Encodingcited by 3
  8. 2025Composable Score-based Graph Diffusion Model for Multi-Conditional Molecular Generationcited by 2
  9. 2026Flowette: Flow Matching with Graphette Priors for Graph Generationcited by 2
  10. 2026Graph-GRPO: Training Graph Flow Models with Reinforcement Learningcited by 2
  11. 2026Variational Learning for Insertion-based Generationcited by 2
  12. 2026Principled Latent Diffusion for Graphs via Laplacian Autoencoderscited by 1
17 more
  1. 2026Variational Bayesian Flow Network for Graph Generationcited by 1
  2. 2026DiPhon: Diffusion on Graphons for Scalable Graph Generationcited by 1
  3. 2025Feature-Aware (Hyper)graph Generation via Next-Scale Predictioncited by 0
  4. 2025FAROS: Fair Graph Generation via Attribute Switching Mechanismscited by 0
  5. 2025Discrete Bayesian Sample Inference for Graph Generationcited by 0
  6. 2025LGDC: Latent Graph Diffusion via Spectrum-Preserving Coarseningcited by 0
  7. 2026GraDE: A Graph Diffusion Estimator for Frequent Subgraph Discovery in Neural Architecturescited by 0
  8. 2026MolHIT: Advancing Molecular-Graph Generation with Hierarchical Discrete Diffusion Modelscited by 0
  9. 2026Balancing Symmetry and Efficiency in Graph Flow Matchingcited by 0
  10. 2026Graph Energy Matching: Transport-Aligned Energy-Based Modeling for Graph Generationcited by 0
  11. 2026Interpolating Discrete Diffusion Models with Controllable Resamplingcited by 0
  12. 2026Scaling Novel Graph Generation via Lightweight Structure-Guided Autoregressive Modelscited by 0
  13. 2026DBMol: Design of High-Affinity, Target-Specific Small Molecules through Structure Prediction Modelscited by 0
  14. 2026TimeRoute: Time-Aware Modality Routing and Diffusion for Multi-Modal Recommendationcited by 0
  15. 2026From topology learning to graph generation: A unifying perspectivecited by 0
  16. 2026Stable Transformers for Graph Generationcited by 0
  17. 2026Higher-Order Molecular Grammars for Generative and Foundation Models in Chemistrycited by 0

Similar, not cited

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  1. 2023SaGess: Sampling Graph Denoising Diffusion Model for Scalable Graph Generation
  2. 2023Conditional Diffusion Based on Discrete Graph Structures for Molecular Graph Generation
  3. 2025Graph Diffusion that can Insert and Delete
  4. 2025Controllable Graph Generation with Diffusion Models via Inference-Time Tree Search Guidance
  5. 2025Simple and Critical Iterative Denoising: A Recasting of Discrete Diffusion in Graph Generation
  6. 2023Generative Diffusion Models on Graphs: Methods and Applications
  7. 2024Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformization
  8. 2026Learning Discrete Diffusion of Graphs via Free-Energy Gradient Flows