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Improving Decoupled Posterior Sampling for Inverse Problems using Data Consistency Constraint

arXiv 2412.00664 ↗First posted 1 Dec 2024cs.LG cs.CV stat.MLcited by 0

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

Abstract (arXiv)

Diffusion models have shown strong performances in solving inverse problems through posterior sampling while they suffer from errors during earlier steps. To mitigate this issue, several Decoupled Posterior Sampling methods have been recently proposed. However, the reverse process in these methods ignores measurement information, leading to errors that impede effective optimization in subsequent steps. To solve this problem, we propose Guided Decoupled Posterior Sampling (GDPS) by integrating a data consistency constraint in the reverse process. The constraint performs a smoother transition within the optimization process, facilitating a more effective convergence toward the target distribution. Furthermore, we extend our method to latent diffusion models and Tweedie's formula, demonstrating its scalability. We evaluate GDPS on the FFHQ and ImageNet datasets across various linear and nonlinear tasks under both standard and challenging conditions. Experimental results demonstrate that GDPS achieves state-of-the-art performance, improving accuracy over existing methods.

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 38 of its 56 references that are in the map. First posted on arXiv 1 Dec 2024.

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38 of 56 references.

Closest ancestors · 17

Same direction, newest first

  1. 2024SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems6 Oct
  2. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing1 Jul
  3. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors29 May
  4. 2024DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Models27 May
  5. 2024Learning Diffusion Priors from Observations by Expectation Maximization22 May
  6. 2023Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion1 Dec
  7. 2023Prompt-tuning latent diffusion models for inverse problems2 Oct
  8. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency16 Jul
  9. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models2 Jul
  10. 2023Direct Diffusion Bridge using Data Consistency for Inverse Problems31 May
  11. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  12. 2023Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems10 Mar
5 more
  1. 2023GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration30 Jan
  2. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems20 Nov
  3. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  4. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
  5. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 21

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  3. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  4. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,177
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  7. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 6,013
  8. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  9. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
  10. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
  11. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
  12. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,043
9 more
  1. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 286
  2. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  3. 2021Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Imagescited by 113
  4. 2024Consistency Flow Matching: Defining Straight Flows with Velocity Consistencycited by 104
  5. 2021Explore Image Deblurring via Blur Kernel Spacecited by 58
  6. 2023Provable Probabilistic Imaging using Score-Based Generative Priorscited by 51
  7. 2021Instance-Optimal Compressed Sensing via Posterior Samplingcited by 43
  8. 2022Quantized Compressed Sensing with Score-based Generative Modelscited by 15
  9. 2013Corrupted Sensing: Novel Guarantees for Separating Structured Signalscited by 7

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