mlsanityData to 7 Oct 2026

BNEM: A Boltzmann Sampler Based on Bootstrapped Noised Energy Matching

arXiv 2409.09787 ↗First posted 15 Sep 2024cs.LG cs.AI stat.COcited by 14

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Abstract (arXiv)

Developing an efficient sampler capable of generating independent and identically distributed (IID) samples from a Boltzmann distribution is a crucial challenge in scientific research, e.g. molecular dynamics. In this work, we intend to learn neural samplers given energy functions instead of data sampled from the Boltzmann distribution. By learning the energies of the noised data, we propose a diffusion-based sampler, Noised Energy Matching, which theoretically has lower variance and more complexity compared to related works. Furthermore, a novel bootstrapping technique is applied to NEM to balance between bias and variance. We evaluate NEM and BNEM on a 2-dimensional 40 Gaussian Mixture Model (GMM) and a 4-particle double-well potential (DW-4). The experimental results demonstrate that BNEM can achieve state-of-the-art performance while being more robust.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 24 of its 52 references that are in the map. First posted on arXiv 15 Sep 2024.

Builds on

24 of 52 references.

References · 24

  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. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  5. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
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  7. 2018Reconciling modern machine learning practice and the bias-variance trade-offcited by 919
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  9. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 248
  10. 2017A Conceptual Introduction to Hamiltonian Monte Carlocited by 207
  11. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 175
  12. 2022An optimal control perspective on diffusion-based generative modelingcited by 145
12 more
  1. 2023Denoising Diffusion Samplerscited by 144
  2. 2023Equivariant flow matchingcited by 131
  3. 2020Learning Energy-Based Models by Diffusion Recovery Likelihoodcited by 122
  4. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 113
  5. 2023Improved sampling via learned diffusionscited by 103
  6. 2021Bayesian Learning via Neural Schr"odinger-F"ollmer Flowscited by 56
  7. 2022Score-Based Diffusion meets Annealed Importance Samplingcited by 51
  8. 2024Improved off-policy training of diffusion samplerscited by 47
  9. 2023Reverse Diffusion Monte Carlocited by 41
  10. 2024Stochastic Localization via Iterative Posterior Samplingcited by 27
  11. 2024Diffusive Gibbs Samplingcited by 21
  12. 2024Iterated Energy-based Flow Matching for Sampling from Boltzmann Densitiescited by 12

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 8; 2026: 6.

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  1. 2025Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Expertscited by 85
  2. 2025No Trick, No Treat: Pursuits and Challenges Towards Simulation-free Training of Neural Samplerscited by 25
  3. 2025Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inferencecited by 22
  4. 2025Progressive Tempering Sampler with Diffusioncited by 13
  5. 2025BoltzNCE: Learning Likelihoods for Boltzmann Generation with Stochastic Interpolants and Noise Contrastive Estimationcited by 7
  6. 2026Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matchingcited by 7
  7. 2025Energy-Weighted Flow Matching: Unlocking Continuous Normalizing Flows for Efficient and Scalable Boltzmann Samplingcited by 6
  8. 2025Neural Flow Samplers with Shortcut Modelscited by 5
  9. 2025Energy-based generator matching: A neural sampler for general state spacecited by 3
  10. 2026Few-Step Boltzmann Generators via Scalable Likelihood Flow Mapscited by 2
  11. 2026Learning Structure, Energy, and Dynamics: A Survey of Artificial Intelligence for Protein Dynamicscited by 1
  12. 2026Semi-supervised Instruction Tuning for Large Language Models on Text-Attributed Graphscited by 0
2 more
  1. 2026Active Learning for Gaussian Process Regression Under Self-Induced Boltzmann Weightscited by 0
  2. 2026Neural Non-Equilibrium Hamiltonian Monte Carlo for Corrected Boltzmann Samplingcited by 0