mlsanityData to 7 Oct 2026

Divergence Triangle for Joint Training of Generator Model, Energy-based Model, and Inference Model

arXiv 1812.10907 ↗First posted 28 Dec 2018stat.ML cs.CV cs.LGcited by 34

Not on the map. Why?

Abstract (arXiv)

This paper proposes the divergence triangle as a framework for joint training of generator model, energy-based model and inference model. The divergence triangle is a compact and symmetric (anti-symmetric) objective function that seamlessly integrates variational learning, adversarial learning, wake-sleep algorithm, and contrastive divergence in a unified probabilistic formulation. This unification makes the processes of sampling, inference, energy evaluation readily available without the need for costly Markov chain Monte Carlo methods. Our experiments demonstrate that the divergence triangle is capable of learning (1) an energy-based model with well-formed energy landscape, (2) direct sampling in the form of a generator network, and (3) feed-forward inference that faithfully reconstructs observed as well as synthesized data. The divergence triangle is a robust training method that can learn from incomplete data.

Key facts. Cited by 34 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Dec 2018.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 6; 2022: 6; 2023: 11; 2024: 5; 2025: 5; 2026: 1.

34 papers.

Sort:

By area:

  1. 2022Latent Diffusion Energy-Based Model for Interpretable Text Modelingcited by 67
  2. 2022A Tale of Two Flows: Cooperative Learning of Langevin Flow and Normalizing Flow Toward Energy-Based Modelcited by 44
  3. 2021Abstract Spatial-Temporal Reasoning via Probabilistic Abduction and Executioncited by 43
  4. 2021JEM++: Improved Techniques for Training JEMcited by 28
  5. 2023Energy-guided Entropic Neural Optimal Transportcited by 25
  6. 2023TEA: Test-time Energy Adaptationcited by 25
  7. 2023Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihoodcited by 19
  8. 2023Energy-Based Models for Anomaly Detection: A Manifold Diffusion Recovery Approachcited by 17
  9. 2022Learning Probabilistic Models from Generator Latent Spaces with Hat EBMcited by 11
  10. 2021Bounds all around: training energy-based models with bidirectional boundscited by 10
  11. 2023Learning Joint Latent Space EBM Prior Model for Multi-layer Generatorcited by 8
  12. 2024Improving Adversarial Energy-Based Model via Diffusion Processcited by 7
22 more
  1. 2021Inferential Wasserstein Generative Adversarial Networkscited by 6
  2. 2022Bi-level Doubly Variational Learning for Energy-based Latent Variable Modelscited by 6
  3. 2023Learning Energy-based Model via Dual-MCMC Teachingcited by 6
  4. 2023Learning Unnormalized Statistical Models via Compositional Optimizationcited by 5
  5. 2025Progressive Test Time Energy Adaptation for Medical Image Segmentationcited by 5
  6. 2023A Hybrid of Generative and Discriminative Models Based on the Gaussian-coupled Softmax Layercited by 4
  7. 2024Maximum Entropy Inverse Reinforcement Learning of Diffusion Models with Energy-Based Modelscited by 4
  8. 2025Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamicscited by 3
  9. 2021Conjugate Energy-Based Modelscited by 2
  10. 2025Learning Energy-Based Generative Models via Potential Flow: A Variational Principle Approach to Probability Density Homotopy Matchingcited by 2
  11. 2023Progressive Energy-Based Cooperative Learning for Multi-Domain Image-to-Image Translationcited by 1
  12. 2024MITA: Bridging the Gap between Model and Data for Test-time Adaptationcited by 1
  13. 2025Learning Energy-based Variational Latent Prior for VAEscited by 1
  14. 2021Deep Consensus Learningcited by 0
  15. 2022EBM Life Cycle: MCMC Strategies for Synthesis, Defense, and Density Modelingcited by 0
  16. 2022EBMs vs. CL: Exploring Self-Supervised Visual Pretraining for Visual Question Answeringcited by 0
  17. 2023STANLEY: Stochastic Gradient Anisotropic Langevin Dynamics for Learning Energy-Based Modelscited by 0
  18. 2023Generalized Contrastive Divergence: Joint Training of Energy-Based Model and Diffusion Model through Inverse Reinforcement Learningcited by 0
  19. 2024Pseudo-label Learning with Calibrated Confidence Using an Energy-based Modelcited by 0
  20. 2024Variational Potential Flow: A Novel Probabilistic Framework for Energy-Based Generative Modellingcited by 0
  21. 2025Exploring bidirectional bounds for minimax-training of Energy-based modelscited by 0
  22. 2026Learning Discrete Autoregressive Priors with Wasserstein Gradient Flowcited by 0