mlsanityData to 7 Oct 2026

MCMC Should Mix: Learning Energy-Based Model with Neural Transport Latent Space MCMC

arXiv 2006.06897 ↗First posted 12 Jun 2020stat.ML cs.LGcited by 25

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Abstract (arXiv)

Learning energy-based model (EBM) requires MCMC sampling of the learned model as an inner loop of the learning algorithm. However, MCMC sampling of EBMs in high-dimensional data space is generally not mixing, because the energy function, which is usually parametrized by a deep network, is highly multi-modal in the data space. This is a serious handicap for both theory and practice of EBMs. In this paper, we propose to learn an EBM with a flow-based model (or in general a latent variable model) serving as a backbone, so that the EBM is a correction or an exponential tilting of the flow-based model. We show that the model has a particularly simple form in the space of the latent variables of the backbone model, and MCMC sampling of the EBM in the latent space mixes well and traverses modes in the data space. This enables proper sampling and learning of EBMs.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Jun 2020.

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Citing papers per year: 2022: 2; 2023: 12; 2024: 6; 2025: 3; 2026: 2.

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  1. 2024EM Distillation for One-step Diffusion Modelscited by 60
  2. 2022Your ViT is Secretly a Hybrid Discriminative-Generative Diffusion Modelcited by 58
  3. 2023Energy-guided Entropic Neural Optimal Transportcited by 25
  4. 2023On Sampling with Approximate Transport Mapscited by 20
  5. 2022End-to-End Stochastic Optimization with Energy-Based Modelcited by 19
  6. 2023Guiding Energy-based Models via Contrastive Latent Variablescited by 17
  7. 2023Energy-Based Models for Anomaly Detection: A Manifold Diffusion Recovery Approachcited by 17
  8. 2023Explaining the effects of non-convergent sampling in the training of Energy-Based Modelscited by 11
  9. 2023Hybrid Energy Based Model in the Feature Space for Out-of-Distribution Detectioncited by 9
  10. 2023Revisiting Energy Based Models as Policies: Ranking Noise Contrastive Estimation and Interpolating Energy Modelscited by 9
  11. 2024Fast training and sampling of Restricted Boltzmann Machinescited by 8
  12. 2023Fast and Functional Structured Data Generators Rooted in Out-of-Equilibrium Physicscited by 7
13 more
  1. 2023Noise-Free Sampling Algorithms via Regularized Wasserstein Proximalscited by 7
  2. 2024Energy based diffusion generator for efficient sampling of Boltzmann distributionscited by 7
  3. 2023Balanced Training of Energy-Based Models with Adaptive Flow Samplingcited by 4
  4. 2025Training Latent Diffusion Models with Interacting Particle Algorithmscited by 4
  5. 2023Energy-Calibrated VAE with Test Time Free Lunchcited by 3
  6. 2025Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamicscited by 3
  7. 2023Latent Space Energy-based Model for Fine-grained Open Set Recognitioncited by 2
  8. 2025Learning Energy-Based Generative Models via Potential Flow: A Variational Principle Approach to Probability Density Homotopy Matchingcited by 2
  9. 2024Hamiltonian Monte Carlo on ReLU Neural Networks is Inefficientcited by 1
  10. 2026LatentFlow: A General Framework for Conditioning Stochastic Processescited by 1
  11. 2024Energy Correction Model in the Feature Space for Out-of-Distribution Detectioncited by 0
  12. 2024Variational Potential Flow: A Novel Probabilistic Framework for Energy-Based Generative Modellingcited by 0
  13. 2026ReFP-AD: Rectified Flow Preconditioning for Energy-Based Anomaly Detectioncited by 0