Simple and Critical Iterative Denoising: A Recasting of Discrete Diffusion in Graph Generation
On the map: Diffusion models → Flow matching, time series and science
Abstract (arXiv)
Discrete Diffusion and Flow Matching models have significantly advanced generative modeling for discrete structures, including graphs. However, the dependencies between intermediate noisy states lead to error accumulation and propagation during the reverse denoising process - a phenomenon known as compounding denoising errors. To address this problem, we propose a novel framework called Simple Iterative Denoising, which simplifies discrete diffusion and circumvents the issue by assuming conditional independence between intermediate states. Additionally, we enhance our model by incorporating a Critic. During generation, the Critic selectively retains or corrupts elements in an instance based on their likelihood under the data distribution. Our empirical evaluations demonstrate that the proposed method significantly outperforms existing discrete diffusion baselines in graph generation tasks.
Key facts. Cited by 10 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 44 of its 55 references that are in the map. First posted on arXiv 27 Mar 2025.
Builds on
44 of 55 references.
Closest ancestors · 10
Same direction, newest first
- 2024Discrete Flow Matching22 Jul
- 2024Variational Flow Matching for Graph Generation7 Jun
- 2024Discrete-state Continuous-time Diffusion for Graph Generation19 May
- 2024Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design7 Feb
- 2024Pard: Permutation-Invariant Autoregressive Diffusion for Graph Generation6 Feb
- 2023Sparse Training of Discrete Diffusion Models for Graph Generation3 Nov
- 2023Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modeling6 May
- 2022Diffusion Models for Graphs Benefit From Discrete State Spaces4 Oct
- 2022DiGress: Discrete Denoising diffusion for graph generation29 Sep
- 2022Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations5 Feb
Other references · 34
- 2020Denoising Diffusion Probabilistic Modelscited by 21,076
- 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
- 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
- 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
- 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,719
- 2022MaskGIT: Masked Generative Image Transformercited by 1,099
- 2017MoleculeNet: A Benchmark for Molecular Machine Learningcited by 1,051
- 2024Simple and Effective Masked Diffusion Language Modelscited by 848
- 2016Automatic chemical design using a data-driven continuous representation of moleculescited by 765
- 2018Junction Tree Variational Autoencoder for Molecular Graph Generationcited by 652
- 2022A Continuous Time Framework for Discrete Denoising Modelscited by 451
- 2018GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Modelscited by 413
22 more
- 2024Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Datacited by 381
- 2020GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generationcited by 305
- 2017Grammar Variational Autoencodercited by 285
- 2022Cold Diffusion: Inverting Arbitrary Image Transforms Without Noisecited by 276
- 2019Efficient Graph Generation with Graph Recurrent Attention Networkscited by 234
- 2025Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusionscited by 214
- 2020Hierarchical Generation of Molecular Graphs using Structural Motifscited by 208
- 2018Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discoverycited by 194
- 2020MoFlow: An Invertible Flow Model for Generating Molecular Graphscited by 185
- 2021GraphDF: A Discrete Flow Model for Molecular Graph Generationcited by 180
- 2023A Reparameterized Discrete Diffusion Model for Text Generationcited by 152
- 2019GraphNVP: An Invertible Flow Model for Generating Molecular Graphscited by 116
- 2019Graph Normalizing Flowscited by 104
- 2022SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generatorscited by 99
- 2025Path Planning for Masked Diffusion Model Samplingcited by 80
- 2020GraphGen: A Scalable Approach to Domain-agnostic Labeled Graph Generationcited by 66
- 2024Think While You Generate: Discrete Diffusion with Planned Denoisingcited by 63
- 2024Informed Correctors for Discrete Diffusion Modelscited by 57
- 2023Graph Generation with Diffusion Mixturecited by 55
- 2023Efficient and Scalable Graph Generation through Iterative Local Expansioncited by 36
- 2023Discrete Graph Auto-Encodercited by 10
- 2024GLAD: Improving Latent Graph Generative Modeling with Simple Quantizationcited by 8
Built on by
Citing papers per year: 2025: 2; 2026: 8.
10 papers.
- 2025Masked Diffusion Models are Secretly Learned-Order Autoregressive Modelscited by 3
- 2026Flowette: Flow Matching with Graphette Priors for Graph Generationcited by 3
- 2026Unrestrained Simplex Denoising for Discrete Data. A Non-Markovian Approach Applied to Graph Generationcited by 2
- 2026Hierarchical Discrete Flow Matching for Graph Generationcited by 2
- 2025Transport-Coupled Bayesian Flows for Molecular Graph Generationcited by 1
- 2026Variational Bayesian Flow Network for Graph Generationcited by 1
- 2026A Systematic Evaluation of Co-folding Model Representations for Small-Molecule Learningcited by 0
- 2026Interpolating Discrete Diffusion Models with Controllable Resamplingcited by 0
- 2026Graph Representation via Elements of Discrete Morse and Cobordism Theoriescited by 0
- 2026MIRRA: Fast, High-Fidelity Molecular Generation with Chemistry-Informed Discrete Flow Matchingcited by 0
- 2026MIRRA: Fast, High-Fidelity Molecular Generation with Chemistry-Informed Discrete Flow Matching12 Oct 2026
- 2026Graph Representation via Elements of Discrete Morse and Cobordism Theories1 Oct 2026
- 2026Interpolating Discrete Diffusion Models with Controllable Resampling19 Apr 2026
- 2026Hierarchical Discrete Flow Matching for Graph Generation31 Mar 2026
- 2026Unrestrained Simplex Denoising for Discrete Data. A Non-Markovian Approach Applied to Graph Generation30 Mar 2026
- 2026Flowette: Flow Matching with Graphette Priors for Graph Generation27 Feb 2026
- 2026A Systematic Evaluation of Co-folding Model Representations for Small-Molecule Learning2 Feb 2026
- 2026Variational Bayesian Flow Network for Graph Generation30 Jan 2026
- 2025Masked Diffusion Models are Secretly Learned-Order Autoregressive Models24 Nov 2025
- 2025Transport-Coupled Bayesian Flows for Molecular Graph Generation11 Oct 2025
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