# MAP-based Problem-Agnostic diffusion model for Inverse Problems

arXiv: https://arxiv.org/abs/2501.15128 · HTML: https://mlsanity.com/paper/2501.15128/

## Key facts

- Cited by 1 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 35 of its 44 references that are in the map.
- First posted on arXiv 25 Jan 2025.

## 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 35)

- [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)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [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)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Deblurring via Stochastic Refinement](https://mlsanity.com/paper/2112.02475/) (2021)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [Manifold Preserving Guided Diffusion](https://mlsanity.com/paper/2311.16424/) (2023)
- [Parallel Diffusion Models of Operator and Image for Blind Inverse Problems](https://mlsanity.com/paper/2211.10656/) (2022)
- [Diffusion Models for Image Restoration and Enhancement: A Comprehensive Survey](https://mlsanity.com/paper/2308.09388/) (2023)
- [An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization](https://mlsanity.com/paper/2404.07771/) (2024)
- [Guidance with Spherical Gaussian Constraint for Conditional Diffusion](https://mlsanity.com/paper/2402.03201/) (2024)
- [Intermediate Layer Optimization for Inverse Problems using Deep Generative Models](https://mlsanity.com/paper/2102.07364/) (2021)
- [Diffusion Models, Image Super-Resolution And Everything: A Survey](https://mlsanity.com/paper/2401.00736/) (2024)
- [Learning Diffusion Priors from Observations by Expectation Maximization](https://mlsanity.com/paper/2405.13712/) (2024)
- [Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems](https://mlsanity.com/paper/2211.12343/) (2022)
- [Diffusion Models and Representation Learning: A Survey](https://mlsanity.com/paper/2407.00783/) (2024)

## Built on by (most cited first, 1 of 1)

- [Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach](https://mlsanity.com/paper/2506.03979/) (2025)

## Abstract (arXiv)

Diffusion models have indeed shown great promise in solving inverse problems in image processing. In this paper, we propose a novel, problem-agnostic diffusion model called the maximum a posteriori (MAP)-based guided term estimation method for inverse problems. To leverage unconditionally pretrained diffusion models to address conditional generation tasks, we divide the conditional score function into two terms according to Bayes' rule: an unconditional score function (approximated by a pretrained score network) and a guided term, which is estimated using a novel MAP-based method that incorporates a Gaussian-type prior of natural images. This innovation allows us to better capture the intrinsic properties of the data, leading to improved performance. Numerical results demonstrate that our method preserves contents more effectively compared to state-of-the-art methods--for example, maintaining the structure of glasses in super-resolution tasks and producing more coherent results in the neighborhood of masked regions during inpainting.