mlsanityData to 7 Oct 2026

Flow-matching -- efficient coarse-graining of molecular dynamics without forces

arXiv 2203.11167 ↗First posted 21 Mar 2022physics.comp-ph cs.LG physics.bio-phcited by 36

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

Abstract (arXiv)

Coarse-grained (CG) molecular simulations have become a standard tool to study molecular processes on time- and length-scales inaccessible to all-atom simulations. Parameterizing CG force fields to match all-atom simulations has mainly relied on force-matching or relative entropy minimization, which require many samples from costly simulations with all-atom or CG resolutions, respectively. Here we present flow-matching, a new training method for CG force fields that combines the advantages of both methods by leveraging normalizing flows, a generative deep learning method. Flow-matching first trains a normalizing flow to represent the CG probability density, which is equivalent to minimizing the relative entropy without requiring iterative CG simulations. Subsequently, the flow generates samples and forces according to the learned distribution in order to train the desired CG free energy model via force matching. Even without requiring forces from the all-atom simulations, flow-matching outperforms classical force-matching by an order of magnitude in terms of data efficiency, and produces CG models that can capture the folding and unfolding transitions of small proteins.

Key facts. Cited by 36 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 30 of its 98 references that are in the map. First posted on arXiv 21 Mar 2022.

Builds on

30 of 98 references.

References · 30

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2013Auto-Encoding Variational Bayescited by 3,980
  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. 2017Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learningcited by 935
  9. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  10. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  11. 2019Neural Spline Flowscited by 590
  12. 2020Directional Message Passing for Molecular Graphscited by 556
18 more
  1. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 381
  2. 2021How to Train Your Energy-Based Modelscited by 271
  3. 2020Stochastic Normalizing Flowscited by 156
  4. 2020Normalizing Flows on Tori and Spherescited by 117
  5. 2020SurVAE Flows: Surjections to Bridge the Gap between VAEs and Flowscited by 71
  6. 2018Machine Learning of coarse-grained Molecular Dynamics Force Fieldscited by 68
  7. 2020Targeted free energy estimation via learned mappingscited by 66
  8. 2020Augmented Normalizing Flows: Bridging the Gap Between Generative Flows and Latent Variable Modelscited by 66
  9. 2020Coarse Graining Molecular Dynamics with Graph Neural Networkscited by 56
  10. 2021Smooth Normalizing Flowscited by 52
  11. 2020VFlow: More Expressive Generative Flows with Variational Data Augmentationcited by 38
  12. 2021Deeptime: a Python library for machine learning dynamical models from time series datacited by 36
  13. 2018Coarse-Graining Auto-Encoders for Molecular Dynamicscited by 30
  14. 2022Generative Coarse-Graining of Molecular Conformationscited by 21
  15. 2019Neural Canonical Transformation with Symplectic Flowscited by 16
  16. 2021Machine Learning Implicit Solvation for Molecular Dynamicscited by 16
  17. 2020Ensemble Learning of Coarse-Grained Molecular Dynamics Force Fields with a Kernel Approachcited by 4
  18. 2021Manifold Density Estimation via Generalized Dequantizationcited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 12; 2024: 10; 2025: 11; 2026: 3.

36 papers.

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  1. 2023Equivariant flow matchingcited by 131
  2. 2024Variational Flow Matching for Graph Generationcited by 78
  3. 2023Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamicscited by 72
  4. 2024Transferable Boltzmann Generatorscited by 43
  5. 2023SE(3) Equivariant Augmented Coupling Flowscited by 37
  6. 2023Str2Str: A Score-based Framework for Zero-shot Protein Conformation Samplingcited by 29
  7. 2023Rigid Body Flows for Sampling Molecular Crystal Structurescited by 27
  8. 2025Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Modelscited by 23
  9. 2023Navigating protein landscapes with a machine-learned transferable coarse-grained modelcited by 22
  10. 2024EquiJump: Protein Dynamics Simulation via SO(3)-Equivariant Stochastic Interpolantscited by 15
  11. 2025Exponential Family Variational Flow Matching for Tabular Data Generationcited by 15
  12. 2023Implicit Transfer Operator Learning: Multiple Time-Resolution Surrogates for Molecular Dynamicscited by 14
24 more
  1. 2024chemtrain: Learning Deep Potential Models via Automatic Differentiation and Statistical Physicscited by 12
  2. 2023DiAMoNDBack: Diffusion-denoising Autoregressive Model for Non-Deterministic Backmapping of Cα Protein Tracescited by 10
  3. 2024Scalable Normalizing Flows Enable Boltzmann Generators for Macromoleculescited by 10
  4. 2023Statistically Optimal Force Aggregation for Coarse-Graining Molecular Dynamicscited by 9
  5. 2025Controlled Generation with Equivariant Variational Flow Matchingcited by 9
  6. 2024Dynamic PDB: A New Dataset and a SE(3) Model Extension by Integrating Dynamic Behaviors and Physical Properties in Protein Structurescited by 8
  7. 2025BoltzNCE: Learning Likelihoods for Boltzmann Generation with Stochastic Interpolants and Noise Contrastive Estimationcited by 7
  8. 2023Latent Representation and Simulation of Markov Processes via Time-Lagged Information Bottleneckcited by 6
  9. 2024Conditional Normalizing Flows for Active Learning of Coarse-Grained Molecular Representationscited by 5
  10. 2023Top-down machine learning of coarse-grained protein force-fieldscited by 4
  11. 2025Purrception: Variational Flow Matching for Vector-Quantized Image Generationcited by 4
  12. 2024AlphaFolding: 4D Diffusion for Dynamic Protein Structure Prediction with Reference and Motion Guidancecited by 3
  13. 2025Beyond Ensembles: Simulating All-Atom Protein Dynamics in a Learned Latent Spacecited by 3
  14. 2025Enhanced Sampling for Efficient Learning of Coarse-Grained Machine Learning Potentialscited by 3
  15. 2025Energy-Based Coarse-Graining in Molecular Dynamics: A Flow-Based Framework without Datacited by 2
  16. 2023Internal-Coordinate Density Modelling of Protein Structure: Covariance Matterscited by 1
  17. 2024Sifting through the Noise: A Survey of Diffusion Probabilistic Models and Their Applications to Biomoleculescited by 1
  18. 2025AI-based Methods for Simulating, Sampling, and Predicting Protein Ensemblescited by 1
  19. 2026Learning Structure, Energy, and Dynamics: A Survey of Artificial Intelligence for Protein Dynamicscited by 1
  20. 2024Efficient Generation of Molecular Clusters with Dual-Scale Equivariant Flow Matchingcited by 0
  21. 2025Operator Forces For Coarse-Grained Molecular Dynamicscited by 0
  22. 2025Scalable learning of macroscopic stochastic dynamicscited by 0
  23. 2026Coarse-Grained Boltzmann Generatorscited by 0
  24. 2026Hessian Matching for Machine-Learned Coarse-Grained Molecular Dynamicscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024F3low: Frame-to-Frame Coarse-grained Molecular Dynamics with SE(3) Guided Flow Matching
  2. 2024Generalized Flow Matching for Transition Dynamics Modeling
  3. 2021Learning Gradient Fields for Molecular Conformation Generation
  4. 2025Path Gradients after Flow Matching
  5. 2025Energy-Based Flow Matching for Generating 3D Molecular Structure
  6. 2022DiffMD: A Geometric Diffusion Model for Molecular Dynamics Simulations
  7. 2024AlphaFold Meets Flow Matching for Generating Protein Ensembles
  8. 2026Generative Pseudo-Force Fields for Molecular Generation