Flow Contrastive Estimation of Energy-Based Models
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Abstract (arXiv)
This paper studies a training method to jointly estimate an energy-based model and a flow-based model, in which the two models are iteratively updated based on a shared adversarial value function. This joint training method has the following traits. (1) The update of the energy-based model is based on noise contrastive estimation, with the flow model serving as a strong noise distribution. (2) The update of the flow model approximately minimizes the Jensen-Shannon divergence between the flow model and the data distribution. (3) Unlike generative adversarial networks (GAN) which estimates an implicit probability distribution defined by a generator model, our method estimates two explicit probabilistic distributions on the data. Using the proposed method we demonstrate a significant improvement on the synthesis quality of the flow model, and show the effectiveness of unsupervised feature learning by the learned energy-based model. Furthermore, the proposed training method can be easily adapted to semi-supervised learning. We achieve competitive results to the state-of-the-art semi-supervised learning methods.
Key facts. Cited by 75 papers in the map (data through 14 Oct 2026). First posted on arXiv 2 Dec 2019.
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Citing papers per year: 2021: 17; 2022: 15; 2023: 22; 2024: 10; 2025: 8; 2026: 3.
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- 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,114
- 2021How to Train Your Energy-Based Modelscited by 274
- 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 252
- 2021Learning to Compose Visual Relationscited by 72
- 2021Unsupervised Learning of Compositional Energy Conceptscited by 71
- 2022A Tale of Two Flows: Cooperative Learning of Langevin Flow and Normalizing Flow Toward Energy-Based Modelcited by 44
- 2021JEM++: Improved Techniques for Training JEMcited by 28
- 2023Energy-guided Entropic Neural Optimal Transportcited by 26
- 2023Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihoodcited by 19
- 2022Adaptive Multi-stage Density Ratio Estimation for Learning Latent Space Energy-based Modelcited by 18
- 2023Guiding Energy-based Models via Contrastive Latent Variablescited by 18
- 2023Energy-Based Models for Anomaly Detection: A Manifold Diffusion Recovery Approachcited by 18
38 more
- 2021On Out-of-distribution Detection with Energy-based Modelscited by 17
- 2021Deep Generative Modeling for Protein Designcited by 17
- 2023EGC: Image Generation and Classification via a Diffusion Energy-Based Modelcited by 16
- 2021Analyzing and Improving the Optimization Landscape of Noise-Contrastive Estimationcited by 15
- 2023Efficient Training of Energy-Based Models Using Jarzynski Equalitycited by 15
- 2022Energy-Based Contrastive Learning of Visual Representationscited by 13
- 2023Learning Energy-Based Prior Model with Diffusion-Amortized MCMCcited by 13
- 2023Provable benefits of annealing for estimating normalizing constants: Importance Sampling, Noise-Contrastive Estimation, and beyondcited by 13
- 2025Density Ratio Estimation with Conditional Probability Pathscited by 13
- 2022The Optimal Noise in Noise-Contrastive Learning Is Not What You Thinkcited by 11
- 2022Learning Probabilistic Models from Generator Latent Spaces with Hat EBMcited by 11
- 2023Revisiting Energy Based Models as Policies: Ranking Noise Contrastive Estimation and Interpolating Energy Modelscited by 10
- 2023Training Energy-Based Models with Diffusion Contrastive Divergencescited by 9
- 2024"Noisier" Noise Contrastive Eestimation is (Almost) Maximum Likelihoodcited by 8
- 2021Identifiable Energy-based Representations: An Application to Estimating Heterogeneous Causal Effectscited by 7
- 2021Pseudo-Spherical Contrastive Divergencecited by 7
- 2022Contrastive Learning of Coarse-Grained Force Fieldscited by 7
- 2023A Tale of Two Latent Flows: Learning Latent Space Normalizing Flow with Short-run Langevin Flow for Approximate Inferencecited by 7
- 2023Geometry of Score Based Generative Modelscited by 7
- 2023On the Effectiveness of Hybrid Mutual Information Estimationcited by 7
- 2024Improving Adversarial Energy-Based Model via Diffusion Processcited by 7
- 2021Elsa: Energy-based learning for semi-supervised anomaly detectioncited by 6
- 2021Inferential Wasserstein Generative Adversarial Networkscited by 6
- 2022Bi-level Doubly Variational Learning for Energy-based Latent Variable Modelscited by 6
- 2022Pitfalls of Gaussians as a noise distribution in NCEcited by 6
- 2022Gradient-Guided Importance Sampling for Learning Binary Energy-Based Modelscited by 6
- 2023Learning Unnormalized Statistical Models via Compositional Optimizationcited by 6
- 2022Statistical applications of contrastive learningcited by 5
- 2024Hitchhiker's guide on the relation of Energy-Based Models with other generative models, sampling and statistical physics: a comprehensive reviewcited by 5
- 2024A Practical Diffusion Path for Samplingcited by 5
- 2024Entropy-Informed Weighting Channel Normalizing Flow for Deep Generative Modelscited by 5
- 2025Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamicscited by 5
- 2022Masked prediction tasks: a parameter identifiability viewcited by 4
- 2022Your Autoregressive Generative Model Can be Better If You Treat It as an Energy-Based Onecited by 4
- 2024Maximum Entropy Inverse Reinforcement Learning of Diffusion Models with Energy-Based Modelscited by 4
- 2021Contrastive learning of strong-mixing continuous-time stochastic processescited by 3
- 2021Learning Proposals for Practical Energy-Based Regressioncited by 3
- 2023Data-Driven Stochastic Motion Evaluation and Optimization with Image by Spatially-Aligned Temporal Encodingcited by 3
50 most cited of 75 All 75 (JSON)
- 2026ReFP-AD: Rectified Flow Preconditioning for Energy-Based Anomaly Detection3 Aug 2026
- 2026Few-Step Boltzmann Generators via Scalable Likelihood Flow Maps27 Jun 2026
- 2026Learning Energy-Based Models from Stochastic Interpolants using Spatiotemporal Differences26 May 2026
- 2025Adaptive Symmetrization of the KL Divergence14 Nov 2025
- 2025Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamics14 Oct 2025
- 2025Learning Energy-based Variational Latent Prior for VAEs30 Sep 2025
- 2025Time-dependent density estimation using binary classifiers18 Jun 2025
- 2025Jarzynski Reweighting and Sampling Dynamics for Training Energy-Based Models: Theoretical Analysis of Different Transition Kernels9 Jun 2025
- 2025Learning Energy-Based Generative Models via Potential Flow: A Variational Principle Approach to Probability Density Homotopy Matching22 Apr 2025
- 2025From Action Labels to Sets: Rethinking Action Supervision for Imitation Learning from Corrective Feedback11 Feb 2025
- 2025Density Ratio Estimation with Conditional Probability Paths4 Feb 2025
- 2024SoftCVI: Contrastive variational inference with self-generated soft labels22 Jul 2024
38 more
- 2024Variational Potential Flow: A Novel Probabilistic Framework for Energy-Based Generative Modelling21 Jul 2024
- 2024Entropy-Informed Weighting Channel Normalizing Flow for Deep Generative Models6 Jul 2024
- 2024Maximum Entropy Inverse Reinforcement Learning of Diffusion Models with Energy-Based Models30 Jun 2024
- 2024A Practical Diffusion Path for Sampling20 Jun 2024
- 2024Hitchhiker's guide on the relation of Energy-Based Models with other generative models, sampling and statistical physics: a comprehensive review19 Jun 2024
- 2024"Noisier" Noise Contrastive Eestimation is (Almost) Maximum Likelihood27 May 2024
- 2024Energy Correction Model in the Feature Space for Out-of-Distribution Detection15 Mar 2024
- 2024Improving Adversarial Energy-Based Model via Diffusion Process4 Mar 2024
- 2024On the connection between Noise-Contrastive Estimation and Contrastive Divergence26 Feb 2024
- 2023Energy-Calibrated VAE with Test Time Free Lunch7 Nov 2023
- 2023Energy-Based Models for Anomaly Detection: A Manifold Diffusion Recovery Approach28 Oct 2023
- 2023STANLEY: Stochastic Gradient Anisotropic Langevin Dynamics for Learning Energy-Based Models19 Oct 2023
- 2023Provable benefits of annealing for estimating normalizing constants: Importance Sampling, Noise-Contrastive Estimation, and beyond5 Oct 2023
- 2023Learning Energy-Based Prior Model with Diffusion-Amortized MCMC5 Oct 2023
- 2023Revisiting Energy Based Models as Policies: Ranking Noise Contrastive Estimation and Interpolating Energy Models11 Sep 2023
- 2023Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihood10 Sep 2023
- 2023Training Energy-Based Models with Diffusion Contrastive Divergences4 Jul 2023
- 2023Progressive Energy-Based Cooperative Learning for Multi-Domain Image-to-Image Translation26 Jun 2023
- 2023Learning Unnormalized Statistical Models via Compositional Optimization13 Jun 2023
- 2023On the Effectiveness of Hybrid Mutual Information Estimation1 Jun 2023
- 2023Efficient Training of Energy-Based Models Using Jarzynski Equality30 May 2023
- 2023Energy-guided Entropic Neural Optimal Transport12 Apr 2023
- 2023EGC: Image Generation and Classification via a Diffusion Energy-Based Model4 Apr 2023
- 2023Non-Generative Energy Based Models3 Apr 2023
- 2023Adversarially Contrastive Estimation of Conditional Neural Processes23 Mar 2023
- 2023Guiding Energy-based Models via Contrastive Latent Variables6 Mar 2023
- 2023Data-Driven Stochastic Motion Evaluation and Optimization with Image by Spatially-Aligned Temporal Encoding10 Feb 2023
- 2023Geometry of Score Based Generative Models9 Feb 2023
- 2023Divide and Compose with Score Based Generative Models5 Feb 2023
- 2023Optimizing the Noise in Self-Supervised Learning: from Importance Sampling to Noise-Contrastive Estimation23 Jan 2023
- 2023A Tale of Two Latent Flows: Learning Latent Space Normalizing Flow with Short-run Langevin Flow for Approximate Inference23 Jan 2023
- 2022Self-Adapting Noise-Contrastive Estimation for Energy-Based Models3 Nov 2022
- 2022Learning Probabilistic Models from Generator Latent Spaces with Hat EBM29 Oct 2022
- 2022Gradient-Guided Importance Sampling for Learning Binary Energy-Based Models11 Oct 2022
- 2022Pitfalls of Gaussians as a noise distribution in NCE1 Oct 2022
- 2022Adaptive Multi-stage Density Ratio Estimation for Learning Latent Space Energy-based Model19 Sep 2022
- 2022Diffusion Models: A Comprehensive Survey of Methods and Applications2 Sep 2022
- 2022Your Autoregressive Generative Model Can be Better If You Treat It as an Energy-Based One26 Jun 2022
50 newest of 75 All 75 (JSON)
- 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,114
- 2023Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihoodcited by 19
- 2023Revisiting Energy Based Models as Policies: Ranking Noise Contrastive Estimation and Interpolating Energy Modelscited by 10
- 2023Geometry of Score Based Generative Modelscited by 7
- 2024A Practical Diffusion Path for Samplingcited by 5
- 2024Maximum Entropy Inverse Reinforcement Learning of Diffusion Models with Energy-Based Modelscited by 4
- 2023Divide and Compose with Score Based Generative Modelscited by 0
- 2026ReFP-AD: Rectified Flow Preconditioning for Energy-Based Anomaly Detectioncited by 0
- 2026ReFP-AD: Rectified Flow Preconditioning for Energy-Based Anomaly Detection3 Aug 2026
- 2024Maximum Entropy Inverse Reinforcement Learning of Diffusion Models with Energy-Based Models30 Jun 2024
- 2024A Practical Diffusion Path for Sampling20 Jun 2024
- 2023Revisiting Energy Based Models as Policies: Ranking Noise Contrastive Estimation and Interpolating Energy Models11 Sep 2023
- 2023Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihood10 Sep 2023
- 2023Geometry of Score Based Generative Models9 Feb 2023
- 2023Divide and Compose with Score Based Generative Models5 Feb 2023
- 2022Diffusion Models: A Comprehensive Survey of Methods and Applications2 Sep 2022
- 2021How to Train Your Energy-Based Modelscited by 274
- 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 252
- 2021Learning to Compose Visual Relationscited by 72
- 2021Unsupervised Learning of Compositional Energy Conceptscited by 71
- 2022A Tale of Two Flows: Cooperative Learning of Langevin Flow and Normalizing Flow Toward Energy-Based Modelcited by 44
- 2021JEM++: Improved Techniques for Training JEMcited by 28
- 2023Energy-guided Entropic Neural Optimal Transportcited by 26
- 2022Adaptive Multi-stage Density Ratio Estimation for Learning Latent Space Energy-based Modelcited by 18
- 2023Guiding Energy-based Models via Contrastive Latent Variablescited by 18
- 2023Energy-Based Models for Anomaly Detection: A Manifold Diffusion Recovery Approachcited by 18
- 2021On Out-of-distribution Detection with Energy-based Modelscited by 17
- 2021Deep Generative Modeling for Protein Designcited by 17
12 most cited of 66 All 66 (JSON)
- 2026Few-Step Boltzmann Generators via Scalable Likelihood Flow Maps27 Jun 2026
- 2026Learning Energy-Based Models from Stochastic Interpolants using Spatiotemporal Differences26 May 2026
- 2025Adaptive Symmetrization of the KL Divergence14 Nov 2025
- 2025Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamics14 Oct 2025
- 2025Learning Energy-based Variational Latent Prior for VAEs30 Sep 2025
- 2025Time-dependent density estimation using binary classifiers18 Jun 2025
- 2025Jarzynski Reweighting and Sampling Dynamics for Training Energy-Based Models: Theoretical Analysis of Different Transition Kernels9 Jun 2025
- 2025Learning Energy-Based Generative Models via Potential Flow: A Variational Principle Approach to Probability Density Homotopy Matching22 Apr 2025
- 2025Density Ratio Estimation with Conditional Probability Paths4 Feb 2025
- 2024SoftCVI: Contrastive variational inference with self-generated soft labels22 Jul 2024
- 2024Variational Potential Flow: A Novel Probabilistic Framework for Energy-Based Generative Modelling21 Jul 2024
- 2024Entropy-Informed Weighting Channel Normalizing Flow for Deep Generative Models6 Jul 2024
12 newest of 66 All 66 (JSON)