mlsanityData to 7 Oct 2026

Equivariant Diffusion for Molecule Generation in 3D

arXiv 2203.17003 ↗First posted 31 Mar 2022cs.LG q-bio.QM stat.MLcited by 666

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

Abstract (arXiv)

This work introduces a diffusion model for molecule generation in 3D that is equivariant to Euclidean transformations. Our E(3) Equivariant Diffusion Model (EDM) learns to denoise a diffusion process with an equivariant network that jointly operates on both continuous (atom coordinates) and categorical features (atom types). In addition, we provide a probabilistic analysis which admits likelihood computation of molecules using our model. Experimentally, the proposed method significantly outperforms previous 3D molecular generative methods regarding the quality of generated samples and efficiency at training time.

Key facts. Cited by 666 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 39 of its 53 references that are in the map. First posted on arXiv 31 Mar 2022.

Builds on

39 of 53 references.

Closest ancestors · 1

Same direction, newest first

  1. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation6 Mar

Other references · 38

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  4. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  5. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  6. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  7. 2021Variational Diffusion Modelscited by 1,145
  8. 2021E(n) Equivariant Graph Neural Networkscited by 951
  9. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  10. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  11. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 566
  12. 2020Directional Message Passing for Molecular Graphscited by 556
26 more
  1. 2018MolGAN: An implicit generative model for small molecular graphscited by 392
  2. 2018GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoderscited by 375
  3. 2018Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generationcited by 363
  4. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  5. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  6. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 248
  7. 2020GEOM: Energy-annotated molecular conformations for property prediction and molecular generationcited by 238
  8. 2019Efficient Graph Generation with Graph Recurrent Attention Networkscited by 231
  9. 2018Constrained Graph Variational Autoencoders for Molecule Designcited by 182
  10. 2019Symmetry-adapted generation of 3d point sets for the targeted discovery of moleculescited by 171
  11. 2021E(n) Equivariant Normalizing Flowscited by 165
  12. 2021Learning Gradient Fields for Molecular Conformation Generationcited by 162
  13. 2022A 3D Generative Model for Structure-Based Drug Designcited by 148
  14. 2021GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensemblescited by 106
  15. 2021Inverse design of 3d molecular structures with conditional generative neural networkscited by 93
  16. 2019A Generative Model for Molecular Distance Geometrycited by 73
  17. 2021An End-to-End Framework for Molecular Conformation Generation via Bilevel Programmingcited by 59
  18. 2020Symmetry-Aware Actor-Critic for 3D Molecular Designcited by 55
  19. 2021Top-N: Equivariant set and graph generation without exchangeabilitycited by 36
  20. 2020Conditional Set Generation with Transformerscited by 32
  21. 2019A Two-Step Graph Convolutional Decoder for Molecule Generationcited by 25
  22. 2020Learning a Continuous Representation of 3D Molecular Structures with Deep Generative Modelscited by 24
  23. 2019Generating valid Euclidean distance matricescited by 19
  24. 2021A Graph VAE and Graph Transformer Approach to Generating Molecular Graphscited by 16
  25. 2021Anytime Sampling for Autoregressive Models via Ordered Autoencodingcited by 11
  26. 2018Generating equilibrium molecules with deep neural networkscited by 10

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 47; 2023: 144; 2024: 185; 2025: 157; 2026: 133.

666 papers.

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  1. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  2. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  3. 2022DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Modelscited by 924
  4. 2022DiGress: Discrete Denoising diffusion for graph generationcited by 503
  5. 2022A Continuous Time Framework for Discrete Denoising Modelscited by 437
  6. 2023InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generationcited by 387
  7. 2022TabDDPM: Modelling Tabular Data with Diffusion Modelscited by 373
  8. 2022DiffusionDet: Diffusion Model for Object Detectioncited by 354
  9. 2024Retrieval-Augmented Generation for AI-Generated Content: A Surveycited by 352
  10. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
  11. 2022A Survey on Generative Diffusion Modelcited by 238
  12. 2023Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Modelscited by 232
38 more
  1. 2022Diffusion models as plug-and-play priorscited by 230
  2. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 229
  3. 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 216
  4. 2022Structure-based Drug Design with Equivariant Diffusion Modelscited by 213
  5. 2023One Transformer Fits All Distributions in Multi-Modal Diffusion at Scalecited by 185
  6. 2023Geometric Latent Diffusion Models for 3D Molecule Generationcited by 185
  7. 20233D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Predictioncited by 176
  8. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restorationcited by 164
  9. 2023A Reparameterized Discrete Diffusion Model for Text Generationcited by 152
  10. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 147
  11. 2023Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learningcited by 145
  12. 2023Crystal Structure Prediction by Joint Equivariant Diffusioncited by 142
  13. 2024Beyond Autoregression: Discrete Diffusion for Complex Reasoning and Planningcited by 135
  14. 2023Equivariant flow matchingcited by 131
  15. 2022Pre-training via Denoising for Molecular Property Predictioncited by 124
  16. 2024Unlocking Guidance for Discrete State-Space Diffusion and Flow Modelscited by 124
  17. 2022Equivariant 3D-Conditional Diffusion Models for Molecular Linker Designcited by 121
  18. 2022Protein structure generation via folding diffusioncited by 113
  19. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 113
  20. 2024FlowMM: Generating Materials with Riemannian Flow Matchingcited by 105
  21. 2022Diffusion-based Molecule Generation with Informative Prior Bridgescited by 104
  22. 2024TFG: Unified Training-Free Guidance for Diffusion Modelscited by 103
  23. 2024An analytic theory of creativity in convolutional diffusion modelscited by 103
  24. 2022Soft Diffusion: Score Matching for General Corruptionscited by 101
  25. 2023MatterGen: a generative model for inorganic materials designcited by 98
  26. 2023MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generationcited by 96
  27. 2022Exploring Chemical Space with Score-based Out-of-distribution Generationcited by 95
  28. 2024Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Reviewcited by 92
  29. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
  30. 2024Physics-Informed Diffusion Modelscited by 88
  31. 2024DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Designcited by 87
  32. 2024Constrained Synthesis with Projected Diffusion Modelscited by 83
  33. 2023DiffusionDepth: Diffusion Denoising Approach for Monocular Depth Estimationcited by 81
  34. 2022Text Generation with Diffusion Language Models: A Pre-training Approach with Continuous Paragraph Denoisecited by 79
  35. 2023Generative Diffusion Models on Graphs: Methods and Applicationscited by 79
  36. 2024Variational Flow Matching for Graph Generationcited by 78
  37. 2025All-atom Diffusion Transformers: Unified generative modelling of molecules and materialscited by 75
  38. 2023Spontaneous Symmetry Breaking in Generative Diffusion Modelscited by 74

50 most cited of 666 All 666 (JSON)

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  1. 2025D3MES: Diffusion Transformer with multihead equivariant self-attention for 3D molecule generation
  2. 2025Towards Unified and Lossless Latent Space for 3D Molecular Latent Diffusion Modeling
  3. 2023Symphony: Symmetry-Equivariant Point-Centered Spherical Harmonics for 3D Molecule Generation
  4. 2024A survey of probabilistic generative frameworks for molecular simulations
  5. 2025Exploring Molecule Generation Using Latent Space Graph Diffusion
  6. 2024Accelerating the Generation of Molecular Conformations with Progressive Distillation of Equivariant Latent Diffusion Models
  7. 2022DiffMD: A Geometric Diffusion Model for Molecular Dynamics Simulations
  8. 2025Diffusion Models for Molecules: A Survey of Methods and Tasks