mlsanityData to 7 Oct 2026

Improved Contrastive Divergence Training of Energy Based Models

arXiv 2012.01316 ↗First posted 2 Dec 2020cs.LGcited by 127

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Cited by 29 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Contrastive divergence is a popular method of training energy-based models, but is known to have difficulties with training stability. We propose an adaptation to improve contrastive divergence training by scrutinizing a gradient term that is difficult to calculate and is often left out for convenience. We show that this gradient term is numerically significant and in practice is important to avoid training instabilities, while being tractable to estimate. We further highlight how data augmentation and multi-scale processing can be used to improve model robustness and generation quality. Finally, we empirically evaluate stability of model architectures and show improved performance on a host of benchmarks and use cases,such as image generation, OOD detection, and compositional generation.

Key facts. Cited by 127 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Dec 2020.

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Citing papers per year: 2021: 13; 2022: 21; 2023: 37; 2024: 25; 2025: 22; 2026: 9.

127 papers.

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  1. 2022Compositional Visual Generation with Composable Diffusion Modelscited by 619
  2. 2021Implicit Behavioral Cloningcited by 442
  3. 2021How to Train Your Energy-Based Modelscited by 271
  4. 2021Pre-training Molecular Graph Representation with 3D Geometrycited by 248
  5. 2023Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMCcited by 216
  6. 2022Generative Flow Networks for Discrete Probabilistic Modelingcited by 113
  7. 2021GraphEBM: Molecular Graph Generation with Energy-Based Modelscited by 85
  8. 2021Learning to Compose Visual Relationscited by 72
  9. 2021Unsupervised Learning of Compositional Energy Conceptscited by 71
  10. 2022Latent Diffusion Energy-Based Model for Interpretable Text Modelingcited by 67
  11. 2022Molecular Geometry Pretraining with SE(3)-Invariant Denoising Distance Matchingcited by 67
  12. 2021Controllable and Compositional Generation with Latent-Space Energy-Based Modelscited by 64
38 more
  1. 2022Your ViT is Secretly a Hybrid Discriminative-Generative Diffusion Modelcited by 58
  2. 2024Community Forensics: Using Thousands of Generators to Train Fake Image Detectorscited by 50
  3. 2022A Tale of Two Flows: Cooperative Learning of Langevin Flow and Normalizing Flow Toward Energy-Based Modelcited by 44
  4. 2024Compositional Generative Modeling: A Single Model is Not All You Needcited by 41
  5. 2024Learning Iterative Reasoning through Energy Diffusioncited by 36
  6. 2024Deep Generative Models in Robotics: A Survey on Learning from Multimodal Demonstrationscited by 35
  7. 2022Learning Iterative Reasoning through Energy Minimizationcited by 32
  8. 2023Energy-based Models are Zero-Shot Planners for Compositional Scene Rearrangementcited by 30
  9. 2023Energy-Based Cross Attention for Bayesian Context Update in Text-to-Image Diffusion Modelscited by 30
  10. 2025Energy-Based Transformers are Scalable Learners and Thinkerscited by 30
  11. 2024Contractive Diffusion Probabilistic Modelscited by 29
  12. 2023Energy-guided Entropic Neural Optimal Transportcited by 25
  13. 2023TEA: Test-time Energy Adaptationcited by 25
  14. 2025Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modelingcited by 25
  15. 2024Out-of-Distribution Detection with a Single Unconditional Diffusion Modelcited by 22
  16. 2022Stable Deep MRI Reconstruction using Generative Priorscited by 21
  17. 2022End-to-End Stochastic Optimization with Energy-Based Modelcited by 19
  18. 2023Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihoodcited by 19
  19. 2023Binary Latent Diffusioncited by 18
  20. 2025Equilibrium Matching: Generative Modeling with Implicit Energy-Based Modelscited by 18
  21. 2023Guiding Energy-based Models via Contrastive Latent Variablescited by 17
  22. 2023Energy-Based Models for Anomaly Detection: A Manifold Diffusion Recovery Approachcited by 17
  23. 2022ZeroC: A Neuro-Symbolic Model for Zero-shot Concept Recognition and Acquisition at Inference Timecited by 16
  24. 2023EGC: Image Generation and Classification via a Diffusion Energy-Based Modelcited by 16
  25. 2024Language-Driven 6-DoF Grasp Detection Using Negative Prompt Guidancecited by 16
  26. 2022Towards Bridging the Performance Gaps of Joint Energy-based Modelscited by 15
  27. 2023Efficient Training of Energy-Based Models Using Jarzynski Equalitycited by 15
  28. 2023Energy-Based Test Sample Adaptation for Domain Generalizationcited by 14
  29. 2025Mitigating Hallucination Through Theory-Consistent Symmetric Multimodal Preference Optimizationcited by 14
  30. 2023Learning Energy-Based Prior Model with Diffusion-Amortized MCMCcited by 13
  31. 2022Designing Perceptual Puzzles by Differentiating Probabilistic Programscited by 12
  32. 2023Energy-Guided Continuous Entropic Barycenter Estimation for General Costscited by 12
  33. 2022Learning Probabilistic Models from Generator Latent Spaces with Hat EBMcited by 11
  34. 2024Reprogramming Pretrained Target-Specific Diffusion Models for Dual-Target Drug Designcited by 11
  35. 2021Hamiltonian Dynamics with Non-Newtonian Momentum for Rapid Samplingcited by 9
  36. 2023Training Energy-Based Models with Diffusion Contrastive Divergencescited by 9
  37. 2023Energy Discrepancies: A Score-Independent Loss for Energy-Based Modelscited by 9
  38. 2023Revisiting Energy Based Models as Policies: Ranking Noise Contrastive Estimation and Interpolating Energy Modelscited by 9

50 most cited of 127 All 127 (JSON)