mlsanityData to 14 Oct 2026

Equivariant Denoisers Cannot Copy Graphs: Align Your Graph Diffusion Models

arXiv 2405.17656 ↗First posted 27 May 2024cs.LG q-bio.QMcited by 8

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

Abstract (arXiv)

Graph diffusion models, dominant in graph generative modeling, remain underexplored for graph-to-graph translation tasks like chemical reaction prediction. We demonstrate that standard permutation equivariant denoisers face fundamental limitations in these tasks due to their inability to break symmetries in noisy inputs. To address this, we propose aligning input and target graphs to break input symmetries while preserving permutation equivariance in non-matching graph portions. Using retrosynthesis (i.e., the task of predicting precursors for synthesis of a given target molecule) as our application domain, we show how alignment dramatically improves discrete diffusion model performance from 5% to a SOTA-matching 54.7% top-1 accuracy. Code is available at https://github.com/Aalto-QuML/DiffAlign.

Key facts. Cited by 8 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 49 of its 80 references that are in the map. First posted on arXiv 27 May 2024.

Builds on

49 of 80 references.

Closest ancestors · 5

Same direction, newest first

  1. 2023SwinGNN: Rethinking Permutation Invariance in Diffusion Models for Graph Generation4 Jul
  2. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Models30 Jun
  3. 2022DiGress: Discrete Denoising diffusion for graph generation29 Sep
  4. 2022Equivariant Diffusion for Molecule Generation in 3D31 Mar
  5. 2020Permutation Invariant Graph Generation via Score-Based Generative Modeling2 Mar

Other references · 44

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  3. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  5. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
  6. 2016Categorical Reparameterization with Gumbel-Softmaxcited by 2,739
  7. 2022Video Diffusion Modelscited by 2,305
  8. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,979
  9. 2023Consistency Modelscited by 1,822
  10. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,719
  11. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,416
  12. 2023Adversarial Diffusion Distillationcited by 759
32 more
  1. 2020Benchmarking Graph Neural Networkscited by 680
  2. 2020A Generalization of Transformer Networks to Graphscited by 661
  3. 2020A Survey on Knowledge Graphs: Representation, Acquisition and Applicationscited by 643
  4. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 574
  5. 2020Temporal Graph Networks for Deep Learning on Dynamic Graphscited by 530
  6. 2018Molecular Transformer - A Model for Uncertainty-Calibrated Chemical Reaction Predictioncited by 229
  7. 2021Autoregressive Diffusion Modelscited by 210
  8. 2023Parallel Sampling of Diffusion Modelscited by 112
  9. 2022Equivariance with Learned Canonicalization Functionscited by 109
  10. 2020Retrosynthesis Prediction with Conditional Graph Logic Networkcited by 104
  11. 2017Predicting Organic Reaction Outcomes with Weisfeiler-Lehman Networkcited by 103
  12. 2018Learning Multimodal Graph-to-Graph Translation for Molecular Optimizationcited by 88
  13. 2020Molecule Edit Graph Attention Network: Modeling Chemical Reactions as Sequences of Graph Editscited by 88
  14. 2020A Graph to Graphs Framework for Retrosynthesis Predictioncited by 86
  15. 2020RetroXpert: Decompose Retrosynthesis Prediction like a Chemistcited by 68
  16. 2021Permutation invariant graph-to-sequence model for template-free retrosynthesis and reaction predictioncited by 68
  17. 2020Learning Graph Models for Retrosynthesis Predictioncited by 65
  18. 2017"Found in Translation": Predicting Outcomes of Complex Organic Chemistry Reactions using Neural Sequence-to-Sequence Modelscited by 55
  19. 2022Root-aligned SMILES: A Tight Representation for Chemical Reaction Predictioncited by 51
  20. 2024Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariancecited by 44
  21. 2022GraphGDP: Generative Diffusion Processes for Permutation Invariant Graph Generationcited by 43
  22. 2023RetroBridge: Modeling Retrosynthesis with Markov Bridgescited by 36
  23. 2020Finding Symmetry Breaking Order Parameters with Euclidean Neural Networkscited by 30
  24. 2023User-defined Event Sampling and Uncertainty Quantification in Diffusion Models for Physical Dynamical Systemscited by 30
  25. 2023Re-evaluating Retrosynthesis Algorithms with Syntheseuscited by 27
  26. 2020Energy-based View of Retrosynthesiscited by 24
  27. 2021Multiset-Equivariant Set Prediction with Approximate Implicit Differentiationcited by 17
  28. 2023Retrosynthesis Prediction with Local Template Retrievalcited by 16
  29. 2023AbODE: Ab Initio Antibody Design using Conjoined ODEscited by 15
  30. 2022FusionRetro: Molecule Representation Fusion via In-Context Learning for Retrosynthetic Planningcited by 14
  31. 2023RetroDiff: Retrosynthesis as Multi-stage Distribution Interpolationcited by 7
  32. 2022G2GT: Retrosynthesis Prediction with Graph to Graph Attention Neural Network and Self-Trainingcited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 1; 2026: 6.

8 papers.

  1. 2025RETRO SYNFLOW: Discrete Flow Matching for Accurate and Diverse Single-Step Retrosynthesiscited by 6
  2. 2024Diffusion Twigs with Loop Guidance for Conditional Graph Generationcited by 4
  3. 2026Principled Latent Diffusion for Graphs via Laplacian Autoencoderscited by 4
  4. 2026The information geometry of product-reference discrete diffusion: Interaction growth complexity and optimal schedulingcited by 2
  5. 2026Representation-Guided Discrete Molecular Graph Retrosynthesiscited by 0
  6. 2026RetroGEF: Dynamic Graph Edit Flow for Single-Step Retrosynthesiscited by 0
  7. 2026Coverage Before Control: Route-Instruction Grounding and Steering for Controllable Retrosynthesiscited by 0
  8. 2026Your Discrete Graph Diffusion Model is Secretly Memorizingcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation
  2. 2026Balancing Symmetry and Efficiency in Graph Flow Matching
  3. 2022Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations
  4. 2025Rao-Blackwell Gradient Estimators for Equivariant Denoising Diffusion
  5. 2025Scalable Non-Equivariant 3D Molecule Generation via Rotational Alignment
  6. 2023Autoregressive Diffusion Model for Graph Generation
  7. 2023Graph Generation with Diffusion Mixture
  8. 2026Efficient Graph Generation via Direct Prediction and Flow Matching