mlsanityData to 7 Oct 2026

Solving Linear Inverse Problems using Higher-Order Annealed Langevin Diffusion

arXiv 2305.05014 ↗First posted 8 May 2023stat.ML eess.SPcited by 6

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Abstract (arXiv)

We propose a solution for linear inverse problems based on higher-order Langevin diffusion. More precisely, we propose pre-conditioned second-order and third-order Langevin dynamics that provably sample from the posterior distribution of our unknown variables of interest while being computationally more efficient than their first-order counterpart and the non-conditioned versions of both dynamics. Moreover, we prove that both pre-conditioned dynamics are well-defined and have the same unique invariant distributions as the non-conditioned cases. We also incorporate an annealing procedure that has the double benefit of further accelerating the convergence of the algorithm and allowing us to accommodate the case where the unknown variables are discrete. Numerical experiments in two different tasks in communications (MIMO symbol detection and channel estimation) and in three tasks for images showcase the generality of our method and illustrate the high performance achieved relative to competing approaches (including learning-based ones) while having comparable or lower computational complexity.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 36 of its 71 references that are in the map. First posted on arXiv 8 May 2023.

Builds on

36 of 71 references.

References · 36

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24 more
  1. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusioncited by 230
  2. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  3. 2015A Complete Recipe for Stochastic Gradient MCMCcited by 146
  4. 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 131
  5. 2022Parallel Diffusion Models of Operator and Image for Blind Inverse Problemscited by 113
  6. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 96
  7. 2017Learned D-AMP: Principled Neural Network based Compressive Image Recoverycited by 65
  8. 2018On sampling from a log-concave density using kinetic Langevin diffusionscited by 61
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  13. 2022Theoretical Perspectives on Deep Learning Methods in Inverse Problemscited by 22
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  17. 2022Annealed Langevin Dynamics for Massive MIMO Detectioncited by 16
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  20. 2022Graph-based Algorithm Unfolding for Energy-aware Power Allocation in Wireless Networkscited by 5
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 2; 2026: 2.

6 papers.

  1. 2024Provable Benefit of Annealed Langevin Monte Carlo for Non-log-concave Samplingcited by 23
  2. 2024Repulsive Latent Score Distillation for Solving Inverse Problemscited by 15
  3. 2025Non-Identical Diffusion Models in MIMO-OFDM Channel Generationcited by 1
  4. 2025Generative Diffusion Model Driven Massive Random Access in Massive MIMO Systemscited by 0
  5. 2026Dimension-Uniform Discretization Analysis of Preconditioned Annealed Langevin Dynamics for Multimodal Gaussian Mixturescited by 0
  6. 2026Generator-Guided Inverse Sampling for L'evy-Driven Generative Modelscited by 0