mlsanityData to 14 Oct 2026

Annealed Langevin Posterior Sampling (ALPS): A Rapid Algorithm for Image Restoration with Multiscale Energy Models

arXiv 2601.02594 ↗First posted 5 Jan 2026eess.IV cs.AI cs.CVcited by 0

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

Abstract (arXiv)

Solving inverse problems in imaging requires models that support efficient inference, uncertainty quantification, and principled probabilistic reasoning. Energy-Based Models (EBMs), with their interpretable energy landscapes and compositional structure, are well-suited for this task but have historically suffered from high computational costs and training instability. To overcome the historical shortcomings of EBMs, we introduce a fast distillation strategy to transfer the strengths of pre-trained diffusion models into multi-scale EBMs. These distilled EBMs enable efficient sampling and preserve the interpretability and compositionality inherent to potential-based frameworks. Leveraging EBM compositionality, we propose Annealed Langevin Posterior Sampling (ALPS) algorithm for Maximum-A-Posteriori (MAP), Minimum Mean Square Error (MMSE), and uncertainty estimates for inverse problems in imaging. Unlike diffusion models that use complex guidance strategies for latent variables, we perform annealing on static posterior distributions that are well-defined and composable. Experiments on image inpainting and MRI reconstruction demonstrate that our method matches or surpasses diffusion-based baselines in both accuracy and efficiency, while also supporting MAP recovery. Overall, our framework offers a scalable and principled solution for inverse problems in imaging, with potential for practical deployment in scientific and clinical settings. ALPS code is available at the GitHub repository hrefhttps://github.com/JyoChand/ALPSALPS.

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 32 of its 39 references that are in the map. First posted on arXiv 5 Jan 2026.

Builds on

32 of 39 references.

Closest ancestors · 4

Same direction, newest first

  1. 2024A Survey on Diffusion Models for Inverse Problems30 Sep
  2. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing1 Jul
  3. 2024Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Data13 Mar
  4. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep

Other references · 28

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  2. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
  3. 2023Consistency Modelscited by 1,822
  4. 2021Variational Diffusion Modelscited by 1,153
  5. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,043
  6. 2022On Distillation of Guided Diffusion Modelscited by 725
  7. 2019Your Classifier is Secretly an Energy Based Model and You Should Treat it Like Onecited by 405
  8. 2020Improved Contrastive Divergence Training of Energy Based Modelscited by 130
  9. 2020Learning Energy-Based Models by Diffusion Recovery Likelihoodcited by 123
  10. 2021Gradient Step Denoiser for convergent Plug-and-Playcited by 108
  11. 2020Learning Latent Space Energy-Based Prior Modelcited by 104
  12. 2020VAEBM: A Symbiosis between Variational Autoencoders and Energy-based Modelscited by 104
16 more
  1. 2020Generalized Energy Based Modelscited by 73
  2. 2020No MCMC for me: Amortized sampling for fast and stable training of energy-based modelscited by 64
  3. 2022A Tale of Two Flows: Cooperative Learning of Langevin Flow and Normalizing Flow Toward Energy-Based Modelcited by 44
  4. 2020Learning Energy-Based Model with Variational Auto-Encoder as Amortized Samplercited by 43
  5. 2020Joint Training of Variational Auto-Encoder and Latent Energy-Based Modelcited by 30
  6. 2019Learning Energy-Based Models in High-Dimensional Spaces with Multi-scale Denoising Score Matchingcited by 26
  7. 2024Relational Diffusion Distillation for Efficient Image Generationcited by 24
  8. 2025Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlocited by 20
  9. 2022Adaptive Multi-stage Density Ratio Estimation for Learning Latent Space Energy-based Modelcited by 18
  10. 2023Guiding Energy-based Models via Contrastive Latent Variablescited by 18
  11. 2023EGC: Image Generation and Classification via a Diffusion Energy-Based Modelcited by 16
  12. 2022Learning Probabilistic Models from Generator Latent Spaces with Hat EBMcited by 11
  13. 2023Multi-Scale Energy (MuSE) plug and play framework for inverse problemscited by 8
  14. 2025Preconditioned Langevin Dynamics with Score-Based Generative Models for Infinite-Dimensional Linear Bayesian Inverse Problemscited by 5
  15. 2025Energy-based models for inverse imaging problemscited by 4
  16. 2021Continuation methods for Riemannian Optimizationcited by 1

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  4. 2026Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors
  5. 2026Discrete Langevin-Inspired Posterior Sampling
  6. 2025DAPS++: Rethinking Diffusion Inverse Problems with Decoupled Posterior Annealing
  7. 2024Posterior sampling via Langevin dynamics based on generative priors
  8. 2026U-DAVI: Uncertainty-Aware Diffusion-Prior-Based Amortized Variational Inference for Image Reconstruction