mlsanityData to 7 Oct 2026

Deep Energy Estimator Networks

arXiv 1805.08306 ↗First posted 21 May 2018stat.ML cs.LGcited by 34

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Abstract (arXiv)

Density estimation is a fundamental problem in statistical learning. This problem is especially challenging for complex high-dimensional data due to the curse of dimensionality. A promising solution to this problem is given here in an inference-free hierarchical framework that is built on score matching. We revisit the Bayesian interpretation of the score function and the Parzen score matching, and construct a multilayer perceptron with a scalable objective for learning the energy (i.e. the unnormalized log-density), which is then optimized with stochastic gradient descent. In addition, the resulting deep energy estimator network (DEEN) is designed as products of experts. We present the utility of DEEN in learning the energy, the score function, and in single-step denoising experiments for synthetic and high-dimensional data. We also diagnose stability problems in the direct estimation of the score function that had been observed for denoising autoencoders.

Key facts. Cited by 34 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 May 2018.

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Citing papers per year: 2020: 1; 2021: 8; 2022: 7; 2023: 8; 2024: 5; 2025: 5.

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  1. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
  2. 2021Score-based Generative Modeling in Latent Spacecited by 634
  3. 2022Understanding Diffusion Models: A Unified Perspectivecited by 337
  4. 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 251
  5. 2022Diffusion Models for Video Prediction and Infillingcited by 134
  6. 2022SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusioncited by 125
  7. 2023A Complete Survey on Generative AI (AIGC): Is ChatGPT from GPT-4 to GPT-5 All You Need?cited by 84
  8. 2021Estimating High Order Gradients of the Data Distribution by Denoisingcited by 63
  9. 2024Optimal score estimation via empirical Bayes smoothingcited by 60
  10. 2021Diffusion-Based Representation Learningcited by 57
  11. 2020Energy-Based Imitation Learningcited by 39
  12. 2023Protein Discovery with Discrete Walk-Jump Samplingcited by 38
22 more
  1. 2023Probabilistic Adaptation of Text-to-Video Modelscited by 29
  2. 2021Arbitrary Conditional Distributions with Energycited by 22
  3. 2023Semi-Implicit Variational Inference via Score Matchingcited by 19
  4. 2025Learning normalized image densities via dual score matchingcited by 17
  5. 2022On Investigating the Conservative Property of Score-Based Generative Modelscited by 16
  6. 2024Aligning Diffusion Behaviors with Q-functions for Efficient Continuous Controlcited by 12
  7. 2022From Points to Functions: Infinite-dimensional Representations in Diffusion Modelscited by 11
  8. 2024Building Minimal and Reusable Causal State Abstractions for Reinforcement Learningcited by 11
  9. 2021Multimeasurement Generative Modelscited by 8
  10. 2025Anomaly Detection and Generation with Diffusion Models: A Surveycited by 8
  11. 2022PnP-ReG: Learned Regularizing Gradient for Plug-and-Play Gradient Descentcited by 7
  12. 2023Moment Matching Denoising Gibbs Samplingcited by 7
  13. 2023Universal Smoothed Score Functions for Generative Modelingcited by 5
  14. 2025ProtFlow: Fast Protein Sequence Design via Flow Matching on Compressed Protein Language Model Embeddingscited by 4
  15. 2023Persistently Trained, Diffusion-assisted Energy-based Modelscited by 3
  16. 2022Knowledge Transfer in Deep Reinforcement Learning for Slice-Aware Mobility Robustness Optimizationcited by 2
  17. 2021Automatic design of novel potential 3CLpro and PLpro inhibitorscited by 0
  18. 2023Diffusion Based Causal Representation Learningcited by 0
  19. 2024Diffusion Generative Modelling for Divide-and-Conquer MCMCcited by 0
  20. 2024Density Estimation via Binless Multidimensional Integrationcited by 0
  21. 2025Distributional Shrinkage I: Universal Denoiser Beyond Tweedie's Formulacited by 0
  22. 2025Distributional Shrinkage II: Higher-Order Scores Encode Brenier Mapcited by 0