mlsanityData to 14 Oct 2026

Deep End-to-End Posterior ENergy (DEEPEN) for image recovery

arXiv 2503.17244 ↗First posted 21 Mar 2025eess.IV cs.CV cs.LGcited by 0

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

Abstract (arXiv)

Current end-to-end (E2E) and plug-and-play (PnP) image reconstruction algorithms approximate the maximum a posteriori (MAP) estimate but cannot offer sampling from the posterior distribution, like diffusion models. By contrast, it is challenging for diffusion models to be trained in an E2E fashion. This paper introduces a Deep End-to-End Posterior ENergy (DEEPEN) framework, which enables MAP estimation as well as sampling. We learn the parameters of the posterior, which is the sum of the data consistency error and the negative log-prior distribution, using maximum likelihood optimization in an E2E fashion. The proposed approach does not require algorithm unrolling, and hence has a smaller computational and memory footprint than current E2E methods, while it does not require contraction constraints typically needed by current PnP methods. Our results demonstrate that DEEPEN offers improved performance than current E2E and PnP models in the MAP setting, while it also offers faster sampling compared to diffusion models. In addition, the learned energy-based model is observed to be more robust to changes in image acquisition settings.

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 22 of its 37 references that are in the map. First posted on arXiv 21 Mar 2025.

Builds on

22 of 37 references.

Closest ancestors · 2

Same direction, newest first

  1. 2024PnP-Flow: Plug-and-Play Image Restoration with Flow Matching3 Oct
  2. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep

Other references · 20

  1. 2020Denoising Diffusion Implicit Modelscited by 9,781
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  3. 2019Deep Equilibrium Modelscited by 615
  4. 2018fastMRI: An Open Dataset and Benchmarks for Accelerated MRIcited by 470
  5. 2019Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processingcited by 421
  6. 2017MoDL: Model Based Deep Learning Architecture for Inverse Problemscited by 387
  7. 2017Learning a Variational Network for Reconstruction of Accelerated MRI Datacited by 342
  8. 2021How to Train Your Energy-Based Modelscited by 274
  9. 2019Plug-and-Play Methods Provably Converge with Properly Trained Denoiserscited by 198
  10. 2021Deep Equilibrium Architectures for Inverse Problems in Imagingcited by 127
  11. 2021Gradient Step Denoiser for convergent Plug-and-Playcited by 108
  12. 2019On the Anatomy of MCMC-Based Maximum Likelihood Learning of Energy-Based Modelscited by 105
8 more
  1. 2019Plug and play methods for magnetic resonance imaging (long version)cited by 75
  2. 2017Plug-and-Play Unplugged: Optimization Free Reconstruction using Consensus Equilibriumcited by 58
  3. 2020MADGAN: unsupervised Medical Anomaly Detection GAN using multiple adjacent brain MRI slice reconstructioncited by 50
  4. 2021CLIP: Cheap Lipschitz Training of Neural Networkscited by 29
  5. 2019Learning Energy-Based Models in High-Dimensional Spaces with Multi-scale Denoising Score Matchingcited by 26
  6. 2023Multi-Scale Energy (MuSE) plug and play framework for inverse problemscited by 8
  7. 2022Memory-efficient model-based deep learning with convergence and robustness guaranteescited by 7
  8. 2024Memory-efficient deep end-to-end posterior network (DEEPEN) for inverse problemscited by 1

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  1. 2026Annealed Langevin Posterior Sampling (ALPS): A Rapid Algorithm for Image Restoration with Multiscale Energy Models
  2. 2026Learning Normalized Energy Models for Linear Inverse Problems
  3. 2020Learning Energy-Based Models by Diffusion Recovery Likelihood
  4. 2026DeepInv: A Novel Self-supervised Learning Approach for Fast and Accurate Diffusion Inversion
  5. 2024Diffusion Priors for Variational Likelihood Estimation and Image Denoising
  6. 2022Denoising Diffusion Restoration Models
  7. 2024Diffusion Posterior Proximal Sampling for Image Restoration
  8. 2024Deep Data Consistency: a Fast and Robust Diffusion Model-based Solver for Inverse Problems