# Solving General Noisy Inverse Problem via Posterior Sampling: A Policy Gradient Viewpoint

arXiv: https://arxiv.org/abs/2403.10585 · HTML: https://mlsanity.com/paper/2403.10585/

## Key facts

- Cited by 5 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 24 of its 32 references that are in the map.
- First posted on arXiv 15 Mar 2024.

## Placed in

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

## Builds on (most cited first, 24 of 24)

- [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)
- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Blended Diffusion for Text-driven Editing of Natural Images](https://mlsanity.com/paper/2111.14818/) (2021)
- [DiffEdit: Diffusion-based semantic image editing with mask guidance](https://mlsanity.com/paper/2210.11427/) (2022)
- [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)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Blended Latent Diffusion](https://mlsanity.com/paper/2206.02779/) (2022)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [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)
- [Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Images](https://mlsanity.com/paper/2106.07009/) (2021)
- [Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems](https://mlsanity.com/paper/2211.12343/) (2022)
- [Explore Image Deblurring via Blur Kernel Space](https://mlsanity.com/paper/2104.00317/) (2021)

## Built on by (most cited first, 5 of 5)

- [Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problems](https://mlsanity.com/paper/2409.20175/) (2024)
- [Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation](https://mlsanity.com/paper/2505.22391/) (2025)
- [Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priors](https://mlsanity.com/paper/2510.10968/) (2025)
- [Constrained Particle Seeking: Solving Diffusion Inverse Problems with Just Forward Passes](https://mlsanity.com/paper/2603.01837/) (2026)
- [Zeroth-Order Non-Log-Concave Sampling with Variance Reduction and Applications to Inverse Problems](https://mlsanity.com/paper/2605.30573/) (2026)

## Abstract (arXiv)

Solving image inverse problems (e.g., super-resolution and inpainting) requires generating a high fidelity image that matches the given input (the low-resolution image or the masked image). By using the input image as guidance, we can leverage a pretrained diffusion generative model to solve a wide range of image inverse tasks without task specific model fine-tuning. To precisely estimate the guidance score function of the input image, we propose Diffusion Policy Gradient (DPG), a tractable computation method by viewing the intermediate noisy images as policies and the target image as the states selected by the policy. Experiments show that our method is robust to both Gaussian and Poisson noise degradation on multiple linear and non-linear inverse tasks, resulting into a higher image restoration quality on FFHQ, ImageNet and LSUN datasets.