mlsanityData to 14 Oct 2026

Learning Normalized Energy Models for Linear Inverse Problems

arXiv 2605.15487 ↗First posted 15 May 2026cs.LG cs.CV eess.IVcited by 0

On the map: Diffusion models → Inverse problems and image restoration

Abstract (arXiv)

Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: (i) the prior density is represented implicitly, and (ii) they rely on likelihood approximations that introduce sampling biases. We address these challenges by introducing a new energy-based model trained for denoising with a covariance-based regularization term that enforces consistency across different measurement conditions. The trained model can compute normalized posterior densities for diverse linear inverse problems, without additional retraining or fine tuning. In addition to preserving the sampling capabilities of diffusion models, this enables previously unavailable capabilities: energy-guided adaptive sampling that adjusts schedules on-the-fly, unbiased Metropolis-Hastings correction steps, and blind estimation of the degradation operator via Bayes rule. We validate the method on multiple datasets (ImageNet, CelebA, AFHQ) and tasks (inpainting, deblurring), demonstrating competitive or superior performance to established baselines.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 47 of its 62 references that are in the map. First posted on arXiv 15 May 2026.

Builds on

47 of 62 references.

Closest ancestors · 11

Same direction, newest first

  1. 2025InvFusion: Bridging Supervised and Zero-shot Diffusion for Inverse Problems2 Apr
  2. 2024A Survey on Diffusion Models for Inverse Problems30 Sep
  3. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing1 Jul
  4. 2024Repulsive Latent Score Distillation for Solving Inverse Problems24 Jun
  5. 2024Generalized Compressed Sensing for Image Reconstruction with Diffusion Probabilistic Models22 May
  6. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  7. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models7 May
  8. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imaging23 Apr
  9. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration20 Mar
  10. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  11. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 36

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  3. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,177
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  5. 2014ImageNet Large Scale Visual Recognition Challengecited by 8,498
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  7. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  8. 2014Deep Learning Face Attributes in the Wildcited by 3,693
  9. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
  10. 2021Palette: Image-to-Image Diffusion Modelscited by 1,300
  11. 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,098
  12. 2017Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learningcited by 950
24 more
  1. 2020Image Quality Assessment: Unifying Structure and Texture Similaritycited by 811
  2. 2024Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusioncited by 681
  3. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 672
  4. 2023Analyzing and Improving the Training Dynamics of Diffusion Modelscited by 402
  5. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 384
  6. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 307
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  9. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 232
  10. 2023Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMCcited by 220
  11. 2022Soft Diffusion: Score Matching for General Corruptionscited by 102
  12. 2022Blurring Diffusion Modelscited by 91
  13. 2024Classifier-Free Guidance is a Predictor-Correctorcited by 84
  14. 2023Diffusion Models With Learned Adaptive Noisecited by 51
  15. 2024Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modellingcited by 45
  16. 2023Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusionscited by 29
  17. 2025Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modelingcited by 27
  18. 2025Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Modelscited by 23
  19. 2025Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlocited by 20
  20. 2025Learning normalized image densities via dual score matchingcited by 18
  21. 2025Joint Distillation for Fast Likelihood Evaluation and Sampling in Flow-based Modelscited by 18
  22. 2024Stochastic Deep Restoration Priors for Imaging Inverse Problemscited by 14
  23. 2025Density Ratio Estimation with Conditional Probability Pathscited by 13
  24. 2025Multitask Learning with Stochastic Interpolantscited by 3

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  4. 2024Learning Diffusion Model from Noisy Measurement using Principled Expectation-Maximization Method
  5. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models
  6. 2024Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance
  7. 2025Zero-Shot Solving of Imaging Inverse Problems via Noise-Refined Likelihood Guided Diffusion Models
  8. 2024Enhancing Diffusion Models for Inverse Problems with Covariance-Aware Posterior Sampling