mlsanityData to 7 Oct 2026

Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics

arXiv 2302.00600 ↗First posted 1 Feb 2023cs.LGcited by 72

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

Abstract (arXiv)

Coarse-grained (CG) molecular dynamics enables the study of biological processes at temporal and spatial scales that would be intractable at an atomistic resolution. However, accurately learning a CG force field remains a challenge. In this work, we leverage connections between score-based generative models, force fields and molecular dynamics to learn a CG force field without requiring any force inputs during training. Specifically, we train a diffusion generative model on protein structures from molecular dynamics simulations, and we show that its score function approximates a force field that can directly be used to simulate CG molecular dynamics. While having a vastly simplified training setup compared to previous work, we demonstrate that our approach leads to improved performance across several small- to medium-sized protein simulations, reproducing the CG equilibrium distribution, and preserving dynamics of all-atom simulations such as protein folding events.

Key facts. Cited by 72 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 24 of its 57 references that are in the map. First posted on arXiv 1 Feb 2023.

Builds on

24 of 57 references.

Closest ancestors · 5

Same direction, newest first

  1. 2022Equivariant 3D-Conditional Diffusion Models for Molecular Linker Design11 Oct
  2. 2022Protein structure generation via folding diffusion30 Sep
  3. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem8 Jun
  4. 2022Equivariant Diffusion for Molecule Generation in 3D31 Mar
  5. 2022Flow-matching -- efficient coarse-graining of molecular dynamics without forces21 Mar

Other references · 19

  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. 2015Variational Inference with Normalizing Flowscited by 2,161
  5. 2016Density estimation using Real NVPcited by 2,029
  6. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  7. 2014NICE: Non-linear Independent Components Estimationcited by 1,052
  8. 2021E(n) Equivariant Graph Neural Networkscited by 951
  9. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
  10. 2021How to Train Your Energy-Based Modelscited by 271
  11. 2021Crystal Diffusion Variational Autoencoder for Periodic Material Generationcited by 268
  12. 2022Torsional Diffusion for Molecular Conformer Generationcited by 262
7 more
  1. 2022Pre-training via Denoising for Molecular Property Predictioncited by 124
  2. 2018Machine Learning of coarse-grained Molecular Dynamics Force Fieldscited by 68
  3. 2020Augmented Normalizing Flows: Bridging the Gap Between Generative Flows and Latent Variable Modelscited by 66
  4. 2020Coarse Graining Molecular Dynamics with Graph Neural Networkscited by 56
  5. 2022The Lie Derivative for Measuring Learned Equivariancecited by 51
  6. 2020VFlow: More Expressive Generative Flows with Variational Data Augmentationcited by 38
  7. 2021Deeptime: a Python library for machine learning dynamical models from time series datacited by 36

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 17; 2024: 24; 2025: 19; 2026: 12.

72 papers.

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  1. 2024AlphaFold Meets Flow Matching for Generating Protein Ensemblescited by 105
  2. 2023Swallowing the Bitter Pill: Simplified Scalable Conformer Generationcited by 55
  3. 2024Target Score Matchingcited by 46
  4. 2023Str2Str: A Score-based Framework for Zero-shot Protein Conformation Samplingcited by 29
  5. 2023Towards Predicting Equilibrium Distributions for Molecular Systems with Deep Learningcited by 26
  6. 2024Diffusion Models in textitDe Novo Drug Designcited by 26
  7. 2025Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Modelscited by 23
  8. 2023Navigating protein landscapes with a machine-learned transferable coarse-grained modelcited by 22
  9. 2024On gauge freedom, conservativity and intrinsic dimensionality estimation in diffusion modelscited by 21
  10. 2025Erwin: A Tree-based Hierarchical Transformer for Large-scale Physical Systemscited by 21
  11. 2024UniGEM: A Unified Approach to Generation and Property Prediction for Moleculescited by 20
  12. 2025Action-Minimization Meets Generative Modeling: Efficient Transition Path Sampling with the Onsager-Machlup Functionalcited by 18
38 more
  1. 2023Score dynamics: scaling molecular dynamics with picoseconds timestep via conditional diffusion modelcited by 16
  2. 2024Structure Language Models for Protein Conformation Generationcited by 16
  3. 2025RNE: plug-and-play diffusion inference-time control and energy-based trainingcited by 16
  4. 2024EquiJump: Protein Dynamics Simulation via SO(3)-Equivariant Stochastic Interpolantscited by 15
  5. 2023Implicit Transfer Operator Learning: Multiple Time-Resolution Surrogates for Molecular Dynamicscited by 14
  6. 2023Towards equilibrium molecular conformation generation with GFlowNetscited by 14
  7. 2024Neural Thermodynamic Integration: Free Energies from Energy-based Diffusion Modelscited by 14
  8. 2025When Scores Learn Geometry: Rate Separations under the Manifold Hypothesiscited by 13
  9. 2024Shallow diffusion networks provably learn hidden low-dimensional structurecited by 12
  10. 2023Denoise Pretraining on Nonequilibrium Molecules for Accurate and Transferable Neural Potentialscited by 11
  11. 2026Enhanced Diffusion Sampling: Efficient Rare Event Sampling and Free Energy Calculation with Diffusion Modelscited by 11
  12. 2023DiAMoNDBack: Diffusion-denoising Autoregressive Model for Non-Deterministic Backmapping of Cα Protein Tracescited by 10
  13. 2023Predicting mutational effects on protein-protein binding via a side-chain diffusion probabilistic modelcited by 9
  14. 2024Flow Matching for Accelerated Simulation of Atomic Transport in Crystalline Materialscited by 9
  15. 2024AdsorbDiff: Adsorbate Placement via Conditional Denoising Diffusioncited by 8
  16. 2024Structured Diffusion Models with Mixture of Gaussians as Prior Distributioncited by 8
  17. 2023CoarsenConf: Equivariant Coarsening with Aggregated Attention for Molecular Conformer Generationcited by 7
  18. 2025ConfRover: Simultaneous Modeling of Protein Conformation and Dynamics via Autoregressioncited by 7
  19. 2023Synthetic pre-training for neural-network interatomic potentialscited by 6
  20. 2023Latent Representation and Simulation of Markov Processes via Time-Lagged Information Bottleneckcited by 6
  21. 2024Zero Shot Molecular Generation via Similarity Kernelscited by 6
  22. 2023Generative artificial intelligence for de novo protein designcited by 5
  23. 2024A Multi-Grained Symmetric Differential Equation Model for Learning Protein-Ligand Binding Dynamicscited by 5
  24. 2025Aligning Protein Conformation Ensemble Generation with Physical Feedbackcited by 5
  25. 2023Top-down machine learning of coarse-grained protein force-fieldscited by 4
  26. 2024JAMUN: Bridging Smoothed Molecular Dynamics and Score-Based Learning for Conformational Ensemblescited by 4
  27. 2024On the design space between molecular mechanics and machine learning force fieldscited by 3
  28. 2024Physical Consistency Bridges Heterogeneous Data in Molecular Multi-Task Learningcited by 3
  29. 2025Distributional Autoencoders Know the Scorecited by 3
  30. 2025Beyond Ensembles: Simulating All-Atom Protein Dynamics in a Learned Latent Spacecited by 3
  31. 2025Enhanced Sampling for Efficient Learning of Coarse-Grained Machine Learning Potentialscited by 3
  32. 2025TEMPO: Temporal Multi-scale Autoregressive Generation of Protein Conformational Ensemblescited by 3
  33. 2026Protein Language Model Embeddings Improve Generalization of Implicit Transfer Operatorscited by 3
  34. 2024Diffusion-based Graph Generative Methodscited by 2
  35. 2024Diff-PIC: Revolutionizing Particle-In-Cell Nuclear Fusion Simulation with Diffusion Modelscited by 2
  36. 2024Constraint Decoupled Latent Diffusion for Protein Backmappingcited by 2
  37. 2023Internal-Coordinate Density Modelling of Protein Structure: Covariance Matterscited by 1
  38. 2023Unbiasing Enhanced Sampling on a High-dimensional Free Energy Surface with Deep Generative Modelcited by 1

50 most cited of 72 All 72 (JSON)

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  1. 2023Backdiff: a diffusion model for generalized transferable protein backmapping
  2. 2024F3low: Frame-to-Frame Coarse-grained Molecular Dynamics with SE(3) Guided Flow Matching
  3. 2021Learning Gradient Fields for Molecular Conformation Generation
  4. 2024Protein Conformation Generation via Force-Guided SE(3) Diffusion Models
  5. 2022Simulate Time-integrated Coarse-grained Molecular Dynamics with Multi-Scale Graph Networks
  6. 2022DiffMD: A Geometric Diffusion Model for Molecular Dynamics Simulations
  7. 2024Context-Guided Diffusion for Out-of-Distribution Molecular and Protein Design
  8. 2025MarS-FM: Generative Modeling of Molecular Dynamics via Markov State Models