mlsanityData to 7 Oct 2026

Iterated Denoising Energy Matching for Sampling from Boltzmann Densities

arXiv 2402.06121 ↗First posted 9 Feb 2024cs.LG stat.MLcited by 113

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Cited by 57 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Efficiently generating statistically independent samples from an unnormalized probability distribution, such as equilibrium samples of many-body systems, is a foundational problem in science. In this paper, we propose Iterated Denoising Energy Matching (iDEM), an iterative algorithm that uses a novel stochastic score matching objective leveraging solely the energy function and its gradient -- and no data samples -- to train a diffusion-based sampler. Specifically, iDEM alternates between (I) sampling regions of high model density from a diffusion-based sampler and (II) using these samples in our stochastic matching objective to further improve the sampler. iDEM is scalable to high dimensions as the inner matching objective, is simulation-free, and requires no MCMC samples. Moreover, by leveraging the fast mode mixing behavior of diffusion, iDEM smooths out the energy landscape enabling efficient exploration and learning of an amortized sampler. We evaluate iDEM on a suite of tasks ranging from standard synthetic energy functions to invariant n-body particle systems. We show that the proposed approach achieves state-of-the-art performance on all metrics and trains 2-5× faster, which allows it to be the first method to train using energy on the challenging 55-particle Lennard-Jones system.

Key facts. Cited by 113 papers in the map (data through 7 Oct 2026). Builds on 48 of its 80 references that are in the map. First posted on arXiv 9 Feb 2024.

Builds on

48 of 80 references.

References · 48

  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. 2022Flow Matching for Generative Modelingcited by 5,426
  5. 2018Neural Ordinary Differential Equationscited by 3,733
  6. 2015Variational Inference with Normalizing Flowscited by 2,161
  7. 2016Density estimation using Real NVPcited by 2,029
  8. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
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  10. 2021E(n) Equivariant Graph Neural Networkscited by 951
  11. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 835
  12. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
36 more
  1. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  2. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 511
  3. 2022Rectified Flow: A Marginal Preserving Approach to Optimal Transportcited by 277
  4. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 248
  5. 2023Self-Consuming Generative Models Go MADcited by 239
  6. 2023SE(3) diffusion model with application to protein backbone generationcited by 214
  7. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 175
  8. 2019Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limitcited by 168
  9. 2021E(n) Equivariant Normalizing Flowscited by 165
  10. 2020Stochastic Normalizing Flowscited by 156
  11. 2019Flow-based generative models for Markov chain Monte Carlo in lattice field theorycited by 147
  12. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 147
  13. 2022An optimal control perspective on diffusion-based generative modelingcited by 145
  14. 2023Denoising Diffusion Samplerscited by 144
  15. 2023Equivariant flow matchingcited by 131
  16. 2022Flow Annealed Importance Sampling Bootstrapcited by 124
  17. 2022Equivariant 3D-Conditional Diffusion Models for Molecular Linker Designcited by 121
  18. 2022GFlowNets and variational inferencecited by 103
  19. 2023Improved sampling via learned diffusionscited by 103
  20. 2023A theory of continuous generative flow networkscited by 98
  21. 2023On the Stability of Iterative Retraining of Generative Models on their own Datacited by 98
  22. 2019Theoretical guarantees for sampling and inference in generative models with latent diffusionscited by 97
  23. 2022Continual Repeated Annealed Flow Transport Monte Carlocited by 66
  24. 2023Timewarp: Transferable Acceleration of Molecular Dynamics by Learning Time-Coarsened Dynamicscited by 62
  25. 2022Score-Based Diffusion meets Annealed Importance Samplingcited by 51
  26. 2018Neural Network Renormalization Groupcited by 48
  27. 2023Geometric Algebra Transformercited by 46
  28. 2023Reverse Diffusion Monte Carlocited by 41
  29. 2021MCMC Variational Inference via Uncorrected Hamiltonian Annealingcited by 39
  30. 2023SE(3) Equivariant Augmented Coupling Flowscited by 37
  31. 2021Monte Carlo Variational Auto-Encoderscited by 36
  32. 2023Rigid Body Flows for Sampling Molecular Crystal Structurescited by 27
  33. 2022Langevin Diffusion Variational Inferencecited by 26
  34. 2023On Sampling with Approximate Transport Mapscited by 20
  35. 2023Improving Gradient-guided Nested Sampling for Posterior Inferencecited by 14
  36. 2021Equivariant Finite Normalizing Flowscited by 11

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 23; 2025: 50; 2026: 40.

113 papers.

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  1. 2025Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Expertscited by 85
  2. 2025Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matchingcited by 78
  3. 2024Amortizing intractable inference in diffusion models for vision, language, and controlcited by 70
  4. 2024NETS: A Non-Equilibrium Transport Samplercited by 67
  5. 2025Efficient Online Reinforcement Learning for Diffusion Policycited by 61
  6. 2024A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimizationcited by 58
  7. 2024Beyond ELBOs: A Large-Scale Evaluation of Variational Methods for Samplingcited by 55
  8. 2025DIME:Diffusion-Based Maximum Entropy Reinforcement Learningcited by 52
  9. 2024Target Score Matchingcited by 46
  10. 2025Scalable Equilibrium Sampling with Sequential Boltzmann Generatorscited by 36
  11. 2026Meta Flow Maps enable scalable reward alignmentcited by 32
  12. 2024Model-Based Diffusion for Trajectory Optimizationcited by 30
38 more
  1. 2025LEAPS: A discrete neural sampler via locally equivariant networkscited by 30
  2. 2025Maximum Entropy Reinforcement Learning with Diffusion Policycited by 29
  3. 2024Steering Masked Discrete Diffusion Models via Discrete Denoising Posterior Predictioncited by 28
  4. 2025Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physicscited by 28
  5. 2025Underdamped Diffusion Bridges with Applications to Samplingcited by 28
  6. 2025Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densitiescited by 26
  7. 2025No Trick, No Treat: Pursuits and Challenges Towards Simulation-free Training of Neural Samplerscited by 25
  8. 2025Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inferencecited by 22
  9. 2024Training Neural Samplers with Reverse Diffusive KL Divergencecited by 21
  10. 2025DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Modelscited by 21
  11. 2025Adjoint Schr"odinger Bridge Samplercited by 20
  12. 2025MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Controlcited by 20
  13. 2025Behavior-Regularized Diffusion Policy Optimization for Offline Reinforcement Learningcited by 18
  14. 2025From discrete-time policies to continuous-time diffusion samplers: Asymptotic equivalences and faster trainingcited by 17
  15. 2025Tilt Matching for Scalable Sampling and Fine-Tuningcited by 17
  16. 2025Outsourced diffusion sampling: Efficient posterior inference in latent spaces of generative modelscited by 16
  17. 2025Proximal Diffusion Neural Samplercited by 16
  18. 2024Sampling from Energy-based Policies using Diffusioncited by 15
  19. 2024BNEM: A Boltzmann Sampler Based on Bootstrapped Noised Energy Matchingcited by 14
  20. 2025Temperature-Annealed Boltzmann Generatorscited by 14
  21. 2024Improving Probabilistic Diffusion Models With Optimal Diagonal Covariance Matchingcited by 13
  22. 2025Accelerated Parallel Tempering via Neural Transportscited by 13
  23. 2025Progressive Tempering Sampler with Diffusioncited by 13
  24. 2024Iterated Energy-based Flow Matching for Sampling from Boltzmann Densitiescited by 12
  25. 2025Posterior Inference with Diffusion Models for High-dimensional Black-box Optimizationcited by 12
  26. 2025FALCON: Few-step Accurate Likelihoods for Continuous Flowscited by 12
  27. 2024Harmonic Path Integral Diffusioncited by 11
  28. 2025Amortized Sampling with Transferable Normalizing Flowscited by 11
  29. 2025On scalable and efficient training of diffusion samplerscited by 10
  30. 2024Markovian Flow Matching: Accelerating MCMC with Continuous Normalizing Flowscited by 9
  31. 2024Learned Reference-based Diffusion Sampling for multi-modal distributionscited by 9
  32. 2025CREPE: Controlling Diffusion with Replica Exchangecited by 9
  33. 2025Non-equilibrium Annealed Adjoint Samplercited by 8
  34. 2024Importance Corrected Neural JKO Samplingcited by 7
  35. 2026Reverse Flow Matching: A Unified Framework for Online Reinforcement Learning with Diffusion and Flow Policiescited by 7
  36. 2026Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matchingcited by 7
  37. 2024Hamiltonian Score Matching and Generative Flowscited by 6
  38. 2025Iterative Importance Fine-tuning of Diffusion Modelscited by 6

50 most cited of 113 All 113 (JSON)