mlsanityData to 7 Oct 2026

MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generation

arXiv 2302.09048 ↗First posted 17 Feb 2023cs.LGcited by 96

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

Abstract (arXiv)

This work introduces MiDi, a novel diffusion model for jointly generating molecular graphs and their corresponding 3D arrangement of atoms. Unlike existing methods that rely on predefined rules to determine molecular bonds based on the 3D conformation, MiDi offers an end-to-end differentiable approach that streamlines the molecule generation process. Our experimental results demonstrate the effectiveness of this approach. On the challenging GEOM-DRUGS dataset, MiDi generates 92% of stable molecules, against 6% for the previous EDM model that uses interatomic distances for bond prediction, and 40% using EDM followed by an algorithm that directly optimize bond orders for validity. Our code is available at github.com/cvignac/MiDi.

Key facts. Cited by 96 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 49 of its 59 references that are in the map. First posted on arXiv 17 Feb 2023.

Builds on

49 of 59 references.

Closest ancestors · 9

Same direction, newest first

  1. 2022Structure-based Drug Design with Equivariant Diffusion Models24 Oct
  2. 2022Equivariant 3D-Conditional Diffusion Models for Molecular Linker Design11 Oct
  3. 2022Diffusion Models for Graphs Benefit From Discrete State Spaces4 Oct
  4. 2022Protein structure generation via folding diffusion30 Sep
  5. 2022DiGress: Discrete Denoising diffusion for graph generation29 Sep
  6. 2022MDM: Molecular Diffusion Model for 3D Molecule Generation13 Sep
  7. 2022Equivariant Diffusion for Molecule Generation in 3D31 Mar
  8. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation6 Mar
  9. 2022Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations5 Feb

Other references · 40

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2020Denoising Diffusion Implicit Modelscited by 9,655
  4. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  6. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 6,979
  7. 2016Layer Normalizationcited by 5,579
  8. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  9. 2022Video Diffusion Modelscited by 2,280
  10. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  11. 2015Spatial Transformer Networkscited by 1,423
  12. 2017MoleculeNet: A Benchmark for Molecular Machine Learningcited by 1,037
28 more
  1. 2021E(n) Equivariant Graph Neural Networkscited by 951
  2. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  3. 2020A Generalization of Transformer Networks to Graphscited by 653
  4. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 566
  5. 2020Principal Neighbourhood Aggregation for Graph Netscited by 477
  6. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  7. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
  8. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 258
  9. 2021Pre-training Molecular Graph Representation with 3D Geometrycited by 248
  10. 2020GEOM: Energy-annotated molecular conformations for property prediction and molecular generationcited by 238
  11. 2019Efficient Graph Generation with Graph Recurrent Attention Networkscited by 231
  12. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  13. 2020Hierarchical Generation of Molecular Graphs using Structural Motifscited by 204
  14. 2018Constrained Graph Variational Autoencoders for Molecule Designcited by 182
  15. 2019Symmetry-adapted generation of 3d point sets for the targeted discovery of moleculescited by 171
  16. 2021E(n) Equivariant Normalizing Flowscited by 165
  17. 20213D Infomax improves GNNs for Molecular Property Predictioncited by 146
  18. 2019GraphNVP: An Invertible Flow Model for Generating Molecular Graphscited by 115
  19. 2022Equivariance with Learned Canonicalization Functionscited by 106
  20. 2022Equivariant Energy-Guided SDE for Inverse Molecular Designcited by 72
  21. 2021Learning to Extend Molecular Scaffolds with Structural Motifscited by 70
  22. 2022MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Designcited by 66
  23. 2022Unified 2D and 3D Pre-Training of Molecular Representationscited by 45
  24. 2022Retrieval-based Controllable Molecule Generationcited by 44
  25. 2022GraphGDP: Generative Diffusion Processes for Permutation Invariant Graph Generationcited by 43
  26. 2021Top-N: Equivariant set and graph generation without exchangeabilitycited by 36
  27. 2022Protein Sequence and Structure Co-Design with Equivariant Translationcited by 31
  28. 2022Set Norm and Equivariant Skip Connections: Putting the Deep in Deep Setscited by 17

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 11; 2024: 23; 2025: 39; 2026: 23.

96 papers.

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By area:

  1. 2024Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Designcited by 294
  2. 2025All-atom Diffusion Transformers: Unified generative modelling of molecules and materialscited by 75
  3. 2023MolDiff: Addressing the Atom-Bond Inconsistency Problem in 3D Molecule Diffusion Generationcited by 65
  4. 2024Mixed Continuous and Categorical Flow Matching for 3D De Novo Molecule Generationcited by 53
  5. 2023Navigating the Design Space of Equivariant Diffusion-Based Generative Models for De Novo 3D Molecule Generationcited by 50
  6. 2023Fast, Expressive SE(n) Equivariant Networks through Weight-Sharing in Position-Orientation Spacecited by 40
  7. 2024SemlaFlow -- Efficient 3D Molecular Generation with Latent Attention and Equivariant Flow Matchingcited by 40
  8. 20233D molecule generation by denoising voxel gridscited by 38
  9. 2023Efficient and Scalable Graph Generation through Iterative Local Expansioncited by 35
  10. 2023Harmonic Self-Conditioned Flow Matching for Multi-Ligand Docking and Binding Site Designcited by 29
  11. 2024A Survey of Generative AI for de novo Drug Design: New Frontiers in Molecule and Protein Generationcited by 29
  12. 2024Cometh: A continuous-time discrete-state graph diffusion modelcited by 29
38 more
  1. 2023Sparse Training of Discrete Diffusion Models for Graph Generationcited by 26
  2. 2024Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structurescited by 20
  3. 2024UniGEM: A Unified Approach to Generation and Property Prediction for Moleculescited by 20
  4. 2025FlowMol3: Flow Matching for 3D De Novo Small-Molecule Generationcited by 20
  5. 2024Structure-based drug design by denoising voxel gridscited by 18
  6. 2025FLOWR: Flow Matching for Structure-Aware De Novo, Interaction- and Fragment-Based Ligand Generationcited by 18
  7. 2024Generative Modelling of Structurally Constrained Graphscited by 17
  8. 2025NExT-Mol: 3D Diffusion Meets 1D Language Modeling for 3D Molecule Generationcited by 17
  9. 2025Multi-domain Distribution Learning for De Novo Drug Designcited by 15
  10. 2024Geometric Representation Condition Improves Equivariant Molecule Generationcited by 13
  11. 2025Applications of Modular Co-Design for De Novo 3D Molecule Generationcited by 13
  12. 2025Equivariant Neural Diffusion for Molecule Generationcited by 13
  13. 2024Geometric-Facilitated Denoising Diffusion Model for 3D Molecule Generationcited by 12
  14. 2025Learning Diffusion Models with Flexible Representation Guidancecited by 12
  15. 2024Exploring Discrete Flow Matching for 3D De Novo Molecule Generationcited by 11
  16. 2025TABASCO: A Fast, Simplified Model for Molecular Generation with Improved Physical Qualitycited by 11
  17. 2023An Equivariant Generative Framework for Molecular Graph-Structure Co-Designcited by 10
  18. 2024Geometry Informed Tokenization of Molecules for Language Model Generationcited by 10
  19. 2023SILVR: Guided Diffusion for Molecule Generationcited by 9
  20. 20243D Vessel Graph Generation Using Denoising Diffusioncited by 9
  21. 2025Controlled Generation with Equivariant Variational Flow Matchingcited by 9
  22. 2024LayerDAG: A Layerwise Autoregressive Diffusion Model for Directed Acyclic Graph Generationcited by 8
  23. 2025Straight-Line Diffusion Model for Efficient 3D Molecular Generationcited by 8
  24. 2025GEOM-Drugs Revisited: Toward More Chemically Accurate Benchmarks for 3D Molecule Generationcited by 8
  25. 2025FreeScene: Mixed Graph Diffusion for 3D Scene Synthesis from Free Promptscited by 8
  26. 2025Unified Guidance for Geometry-Conditioned Molecular Generationcited by 7
  27. 2025Bures-Wasserstein Flow Matching for Graph Generationcited by 7
  28. 2024Zero Shot Molecular Generation via Similarity Kernelscited by 6
  29. 2024E(3)-equivariant models cannot learn chirality: Field-based molecular generationcited by 6
  30. 2025SynCoGen: Synthesizable 3D Molecule Generation via Joint Reaction and Coordinate Modelingcited by 5
  31. 2025Controllable Graph Generation with Diffusion Models via Inference-Time Tree Search Guidancecited by 5
  32. 2026Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generationcited by 5
  33. 2025Graph Diffusion that can Insert and Deletecited by 4
  34. 2025MolGuidance: Advanced Guidance Strategies for Conditional Molecular Generation with Flow Matchingcited by 4
  35. 2024NEBULA: Neural Empirical Bayes Under Latent Representations for Efficient and Controllable Design of Molecular Librariescited by 3
  36. 2025Disentangling Total-Variance and Signal-to-Noise-Ratio Improves Diffusion Modelscited by 3
  37. 2025Clifford Group Equivariant Diffusion Models for 3D Molecular Generationcited by 3
  38. 2025Scalable Non-Equivariant 3D Molecule Generation via Rotational Alignmentcited by 3

50 most cited of 96 All 96 (JSON)

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  1. 2024Diffusion Models in textitDe Novo Drug Design
  2. 2023Coarse-to-Fine: a Hierarchical Diffusion Model for Molecule Generation in 3D
  3. 2023Geometry-Complete Diffusion for 3D Molecule Generation and Optimization
  4. 2025DMol: A Highly Efficient and Chemical Motif-Preserving Molecule Generation Platform
  5. 2025Diffusion Models at the Drug Discovery Frontier: A Review on Generating Small Molecules versus Therapeutic Peptides
  6. 2026Equivariant Asynchronous Diffusion: An Adaptive Denoising Schedule for Accelerated Molecular Conformation Generation
  7. 2025Sampling 3D Molecular Conformers with Diffusion Transformers
  8. 2023Learning Joint 2D & 3D Diffusion Models for Complete Molecule Generation