mlsanityData to 7 Oct 2026

Provable Compressed Sensing with Generative Priors via Langevin Dynamics

arXiv 2102.12643 ↗First posted 25 Feb 2021stat.ML cs.LGcited by 14

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Abstract (arXiv)

Deep generative models have emerged as a powerful class of priors for signals in various inverse problems such as compressed sensing, phase retrieval and super-resolution. Here, we assume an unknown signal to lie in the range of some pre-trained generative model. A popular approach for signal recovery is via gradient descent in the low-dimensional latent space. While gradient descent has achieved good empirical performance, its theoretical behavior is not well understood. In this paper, we introduce the use of stochastic gradient Langevin dynamics (SGLD) for compressed sensing with a generative prior. Under mild assumptions on the generative model, we prove the convergence of SGLD to the true signal. We also demonstrate competitive empirical performance to standard gradient descent.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 25 of its 46 references that are in the map. First posted on arXiv 25 Feb 2021.

Builds on

25 of 46 references.

References · 25

  1. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  2. 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,048
  3. 2016Density estimation using Real NVPcited by 2,029
  4. 2014Image Super-Resolution Using Deep Convolutional Networkscited by 1,218
  5. 2017Deep Image Priorcited by 1,097
  6. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,061
  7. 2017Compressed Sensing using Generative Modelscited by 337
  8. 2020Deep Learning Techniques for Inverse Problems in Imagingcited by 290
  9. 2017Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysiscited by 242
  10. 2019Invertible generative models for inverse problems: mitigating representation error and dataset biascited by 93
  11. 2017A Hitting Time Analysis of Stochastic Gradient Langevin Dynamicscited by 70
  12. 2017One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Modelscited by 67
13 more
  1. 2018Solving Linear Inverse Problems Using GAN Priors: An Algorithm with Provable Guaranteescited by 58
  2. 2020Composing Normalizing Flows for Inverse Problemscited by 48
  3. 2019Deep Compressed Sensingcited by 46
  4. 2017Global Guarantees for Enforcing Deep Generative Priors by Empirical Riskcited by 37
  5. 2019Inverting Deep Generative models, One layer at a timecited by 33
  6. 2017Convergence Rate of Riemannian Hamiltonian Monte Carlo and Faster Polytope Volume Computationcited by 32
  7. 2019Algorithmic Guarantees for Inverse Imaging with Untrained Network Priorscited by 32
  8. 2020Faster Convergence of Stochastic Gradient Langevin Dynamics for Non-Log-Concave Samplingcited by 32
  9. 2020Solving Inverse Problems with a Flow-based Noise Modelcited by 31
  10. 2019Information-Theoretic Lower Bounds for Compressive Sensing with Generative Modelscited by 25
  11. 2017Learning to Invert: Signal Recovery via Deep Convolutional Networkscited by 22
  12. 2019Fast and Provable ADMM for Learning with Generative Priorscited by 18
  13. 2016Sampling Generative Networkscited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 5; 2023: 1; 2024: 3; 2025: 3; 2026: 2.

14 papers.

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  1. 2022Theoretical Perspectives on Deep Learning Methods in Inverse Problemscited by 22
  2. 2022Generative Principal Component Analysiscited by 12
  3. 2022Score-Guided Intermediate Layer Optimization: Fast Langevin Mixing for Inverse Problemscited by 11
  4. 2022Non-Iterative Recovery from Nonlinear Observations using Generative Modelscited by 9
  5. 2022Misspecified Phase Retrieval with Generative Priorscited by 7
  6. 2024Bagged Deep Image Prior for Recovering Images in the Presence of Speckle Noisecited by 4
  7. 2025Multilook Coherent Imaging: Theoretical Guarantees and Algorithmscited by 4
  8. 2024Generalized Eigenvalue Problems with Generative Priorscited by 3
  9. 2025Learning Single Index Models with Diffusion Priorscited by 2
  10. 2023On the Fine-Grained Hardness of Inverting Generative Modelscited by 1
  11. 2025Diffusion Model Based Signal Recovery Under 1-Bit Quantizationcited by 1
  12. 2026Riemannian AmbientFlow: Towards Simultaneous Manifold Learning and Generative Modeling from Corrupted Datacited by 1
2 more
  1. 2024Imaging Signal Recovery Using Neural Network Priors Under Uncertain Forward Model Parameterscited by 0
  2. 2026Measurement Geometry and Design for Trustworthy Generative Inverse Problemscited by 0