# Diffusion Posterior Proximal Sampling for Image Restoration

arXiv: https://arxiv.org/abs/2402.16907 · HTML: https://mlsanity.com/paper/2402.16907/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 38 of its 58 references that are in the map.
- First posted on arXiv 25 Feb 2024.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 30 of 38)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation](https://mlsanity.com/paper/2303.00848/) (2023)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models](https://mlsanity.com/paper/2307.00619/) (2023)
- [Low-Light Image Enhancement with Wavelet-based Diffusion Models](https://mlsanity.com/paper/2306.00306/) (2023)
- [Global Structure-Aware Diffusion Process for Low-Light Image Enhancement](https://mlsanity.com/paper/2310.17577/) (2023)
- [Input Perturbation Reduces Exposure Bias in Diffusion Models](https://mlsanity.com/paper/2301.11706/) (2023)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [Alleviating Exposure Bias in Diffusion Models through Sampling with Shifted Time Steps](https://mlsanity.com/paper/2305.15583/) (2023)
- [Prompt-tuning latent diffusion models for inverse problems](https://mlsanity.com/paper/2310.01110/) (2023)

## Built on by (most cited first, 14 of 14)

- [Diffusion models for inverse problems](https://mlsanity.com/paper/2508.01975/) (2025)
- [Constrained Diffusion with Trust Sampling](https://mlsanity.com/paper/2411.10932/) (2024)
- [Multimodal Atmospheric Super-Resolution With Deep Generative Models](https://mlsanity.com/paper/2506.22780/) (2025)
- [Forecasting When to Forecast: Accelerating Diffusion Models with Confidence-Gated Taylor](https://mlsanity.com/paper/2508.02240/) (2025)
- [Enhancing Diffusion Model Stability for Image Restoration via Gradient Management](https://mlsanity.com/paper/2507.06656/) (2025)
- [Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators](https://mlsanity.com/paper/2512.23463/) (2025)
- [Target-Guided Bayesian Flow Networks for Quantitatively Constrained CAD Generation](https://mlsanity.com/paper/2510.25163/) (2025)
- [Any Image Restoration via Efficient Spatial-Frequency Degradation Adaptation](https://mlsanity.com/paper/2504.14249/) (2025)
- [LatentINDIGO: An INN-Guided Latent Diffusion Algorithm for Image Restoration](https://mlsanity.com/paper/2505.12935/) (2025)
- [Dual Prompt Learning for Adapting Vision-Language Models to Downstream Image-Text Retrieval](https://mlsanity.com/paper/2508.04028/) (2025)
- [A Gradient Flow Approach to Solving Inverse Problems with Latent Diffusion Models](https://mlsanity.com/paper/2509.19276/) (2025)
- [Uncertainty Quantification in HSI Reconstruction using Physics-Aware Diffusion Priors and Optics-Encoded Measurements](https://mlsanity.com/paper/2511.18473/) (2025)
- [MPFlow: Multi-modal Posterior-Guided Flow Matching for Zero-Shot MRI Reconstruction](https://mlsanity.com/paper/2603.03710/) (2026)
- [Consistent and Editable: A Balanced Framework for Text-Guided Video Editing](https://mlsanity.com/paper/2607.05056/) (2026)

## Abstract (arXiv)

Diffusion models have demonstrated remarkable efficacy in generating high-quality samples. Existing diffusion-based image restoration algorithms exploit pre-trained diffusion models to leverage data priors, yet they still preserve elements inherited from the unconditional generation paradigm. These strategies initiate the denoising process with pure white noise and incorporate random noise at each generative step, leading to over-smoothed results. In this paper, we present a refined paradigm for diffusion-based image restoration. Specifically, we opt for a sample consistent with the measurement identity at each generative step, exploiting the sampling selection as an avenue for output stability and enhancement. The number of candidate samples used for selection is adaptively determined based on the signal-to-noise ratio of the timestep. Additionally, we start the restoration process with an initialization combined with the measurement signal, providing supplementary information to better align the generative process. Extensive experimental results and analyses validate that our proposed method significantly enhances image restoration performance while consuming negligible additional computational resources.