mlsanityData to 7 Oct 2026

Gaussian is All You Need: A Unified Framework for Solving Inverse Problems via Diffusion Posterior Sampling

arXiv 2409.08906 ↗First posted 13 Sep 2024eess.IV cs.CVcited by 5

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

Abstract (arXiv)

Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based methods integrate data consistency steps by approximating the likelihood function within the diffusion reverse sampling process. In this paper, we show that the existing approximations are either insufficient or computationally inefficient. To address these issues, we propose a unified likelihood approximation method that incorporates a covariance correction term to enhance the performance and avoids propagating gradients through the diffusion model. The correction term, when integrated into the reverse diffusion sampling process, achieves better convergence towards the true data posterior for selected distributions and improves performance on real-world natural image datasets. Furthermore, we present an efficient way to factorize and invert the covariance matrix of the likelihood function for several inverse problems. Our comprehensive experiments demonstrate the effectiveness of our method over several existing approaches. Code available at https://github.com/CSIPlab/CoDPS.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 32 of its 49 references that are in the map. First posted on arXiv 13 Sep 2024.

Builds on

32 of 49 references.

Closest ancestors · 14

Same direction, newest first

  1. 2024Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance3 Feb
  2. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency16 Jul
  3. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  4. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models7 May
  5. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration20 Mar
  6. 2023DiffIR: Efficient Diffusion Model for Image Restoration16 Mar
  7. 2023Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems10 Mar
  8. 2023GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration30 Jan
  9. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  10. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems20 Nov
  11. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  12. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
2 more
  1. 2022Denoising Diffusion Restoration Models27 Jan
  2. 2021Deblurring via Stochastic Refinement5 Dec

Other references · 18

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  4. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,029
  5. 2020Denoising Diffusion Implicit Modelscited by 9,655
  6. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  7. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  8. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  9. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  10. 2022Generative Adversarial Networkscited by 5,603
  11. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  12. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
6 more
  1. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,419
  2. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,352
  3. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 634
  4. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 244
  5. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  6. 2023Domain Expansion via Network Adaptation for Solving Inverse Problemscited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 4.

5 papers.

  1. 2025Diffusion models for multivariate subsurface generation and efficient probabilistic inversioncited by 1
  2. 2026A Gibbs posterior sampler for inverse problem based on prior diffusion modelcited by 1
  3. 2026Estimation of instrument and noise parameters for inverse problem based on prior diffusion modelcited by 0
  4. 2026Geometry-Correct Diffusion Posterior Sampling with Denoiser-Pullback Curvature Guidance and Manifold-Aligned Dampingcited by 0
  5. 2026Direct Conditional Transition Sampling for Diffusion Inverse Problemscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Exact Evaluation of the Accuracy of Diffusion Models for Inverse Problems with Gaussian Data Distributions
  2. 2025Diffusion models for inverse problems
  3. 2024Enhancing Diffusion Models for Inverse Problems with Covariance-Aware Posterior Sampling
  4. 2024A Survey on Diffusion Models for Inverse Problems
  5. 2024Enhancing Diffusion Posterior Sampling for Inverse Problems by Integrating Crafted Measurements
  6. 2025A Mixture-Based Framework for Guiding Diffusion Models
  7. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models
  8. 2024Prototype Clustered Diffusion Models for Versatile Inverse Problems