# Diffusion Priors for Variational Likelihood Estimation and Image Denoising

arXiv: https://arxiv.org/abs/2410.17521 · HTML: https://mlsanity.com/paper/2410.17521/

## 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 41 of its 53 references that are in the map.
- First posted on arXiv 23 Oct 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 41)

- [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)
- [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)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [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)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (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)
- [Simple diffusion: End-to-end diffusion for high resolution images](https://mlsanity.com/paper/2301.11093/) (2023)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [Exploiting Deep Generative Prior for Versatile Image Restoration and Manipulation](https://mlsanity.com/paper/2003.13659/) (2020)
- [Generative Diffusion Prior for Unified Image Restoration and Enhancement](https://mlsanity.com/paper/2304.01247/) (2023)
- [Neighbor2Neighbor: Self-Supervised Denoising from Single Noisy Images](https://mlsanity.com/paper/2101.02824/) (2021)
- [High-Quality Self-Supervised Deep Image Denoising](https://mlsanity.com/paper/1901.10277/) (2019)
- [Efficient and Explicit Modelling of Image Hierarchies for Image Restoration](https://mlsanity.com/paper/2303.00748/) (2023)
- [Noisier2Noise: Learning to Denoise from Unpaired Noisy Data](https://mlsanity.com/paper/1910.11908/) (2019)
- [Variational Denoising Network: Toward Blind Noise Modeling and Removal](https://mlsanity.com/paper/1908.11314/) (2019)
- [Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Images](https://mlsanity.com/paper/2106.07009/) (2021)
- [Diffusion Models for Image Restoration and Enhancement: A Comprehensive Survey](https://mlsanity.com/paper/2308.09388/) (2023)
- [AP-BSN: Self-Supervised Denoising for Real-World Images via Asymmetric PD and Blind-Spot Network](https://mlsanity.com/paper/2203.11799/) (2022)
- [Blind2Unblind: Self-Supervised Image Denoising with Visible Blind Spots](https://mlsanity.com/paper/2203.06967/) (2022)
- [DR2: Diffusion-based Robust Degradation Remover for Blind Face Restoration](https://mlsanity.com/paper/2303.06885/) (2023)
- [Relay Diffusion: Unifying diffusion process across resolutions for image synthesis](https://mlsanity.com/paper/2309.03350/) (2023)
- [Real-world Noisy Image Denoising: A New Benchmark](https://mlsanity.com/paper/1804.02603/) (2018)
- [A Poisson-Gaussian Denoising Dataset with Real Fluorescence Microscopy Images](https://mlsanity.com/paper/1812.10366/) (2018)
- [Zero-Shot Noise2Noise: Efficient Image Denoising without any Data](https://mlsanity.com/paper/2303.11253/) (2023)
- [C2N: Practical Generative Noise Modeling for Real-World Denoising](https://mlsanity.com/paper/2202.09533/) (2022)

## Abstract (arXiv)

Real-world noise removal is crucial in low-level computer vision. Due to the remarkable generation capabilities of diffusion models, recent attention has shifted towards leveraging diffusion priors for image restoration tasks. However, existing diffusion priors-based methods either consider simple noise types or rely on approximate posterior estimation, limiting their effectiveness in addressing structured and signal-dependent noise commonly found in real-world images. In this paper, we build upon diffusion priors and propose adaptive likelihood estimation and MAP inference during the reverse diffusion process to tackle real-world noise. We introduce an independent, non-identically distributed likelihood combined with the noise precision (inverse variance) prior and dynamically infer the precision posterior using variational Bayes during the generation process. Meanwhile, we rectify the estimated noise variance through local Gaussian convolution. The final denoised image is obtained by propagating intermediate MAP solutions that balance the updated likelihood and diffusion prior. Additionally, we explore the local diffusion prior inherent in low-resolution diffusion models, enabling direct handling of high-resolution noisy images. Extensive experiments and analyses on diverse real-world datasets demonstrate the effectiveness of our method. Code is available at https://github.com/HUST-Tan/DiffusionVI.