# Frequency-Guided Posterior Sampling for Diffusion-Based Image Restoration

arXiv: https://arxiv.org/abs/2411.15295 · HTML: https://mlsanity.com/paper/2411.15295/

## Key facts

- Cited by 11 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 46 references that are in the map.
- First posted on arXiv 22 Nov 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)
- [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)
- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [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)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Exploiting Deep Generative Prior for Versatile Image Restoration and Manipulation](https://mlsanity.com/paper/2003.13659/) (2020)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- ["Double-DIP": Unsupervised Image Decomposition via Coupled Deep-Image-Priors](https://mlsanity.com/paper/1812.00467/) (2018)
- [Guidance with Spherical Gaussian Constraint for Conditional Diffusion](https://mlsanity.com/paper/2402.03201/) (2024)
- [Learning Diffusion Priors from Observations by Expectation Maximization](https://mlsanity.com/paper/2405.13712/) (2024)
- [Score-based Generative Neural Networks for Large-Scale Optimal Transport](https://mlsanity.com/paper/2110.03237/) (2021)

## Built on by (most cited first, 11 of 11)

- [Exploiting the Exact Denoising Posterior Score in Training-Free Guidance of Diffusion Models](https://mlsanity.com/paper/2506.13614/) (2025)
- [MAP-based Problem-Agnostic diffusion model for Inverse Problems](https://mlsanity.com/paper/2501.15128/) (2025)
- [Inference-Time Scaling for Visual AutoRegressive modeling by Searching Representative Samples](https://mlsanity.com/paper/2601.07293/) (2026)
- [Align & Invert: Solving Inverse Problems with Diffusion and Flow-based Models via Representation Alignment](https://mlsanity.com/paper/2511.16870/) (2025)
- [Scale-Cascaded Diffusion Models for Super-Resolution in Medical Imaging](https://mlsanity.com/paper/2601.23201/) (2026)
- [Posterior Continuation with Noise-Conditioned Frequency Exposure for Diffusion Inverse Problems](https://mlsanity.com/paper/2602.00176/) (2026)
- [TAFG-MAN: Timestep-Adaptive Frequency-Gated Latent Diffusion for Efficient and High-Quality Low-Dose CT Image Denoising](https://mlsanity.com/paper/2603.20868/) (2026)
- [ZID-Net: Zero-Inference Diffusion Prior Decoupling Network for Single Image Dehazing](https://mlsanity.com/paper/2604.23709/) (2026)
- [ANaLOG: Anisotropic Native-Latent Operator Guidance for Solving Inverse Problems](https://mlsanity.com/paper/2609.31933/) (2026)
- [FastGuide: Accelerating Reward Guidance for Diffusion Large Language Models](https://mlsanity.com/paper/2609.36202/) (2026)
- [Frequency-Decoupled Diffusion Guidance for Non-Blind Image Deblurring](https://mlsanity.com/paper/2610.06221/) (2026)

## Abstract (arXiv)

Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean reconstruction given the degraded observation. Recently, modern pretrained diffusion models have been used for image restoration by modifying their sampling procedure to account for the degradation process. However, these methods often rely on certain approximations that can lead to significant errors and compromised sample quality. In this paper, we provide the first rigorous analysis of this approximation error for linear inverse problems under distributional assumptions on the space of natural images, demonstrating cases where previous works can fail dramatically. Motivated by our theoretical insights, we propose a simple modification to existing diffusion-based restoration methods. Our approach introduces a time-varying low-pass filter in the frequency domain of the measurements, progressively incorporating higher frequencies during the restoration process. We develop an adaptive curriculum for this frequency schedule based on the underlying data distribution. Our method significantly improves performance on challenging image restoration tasks including motion deblurring and image dehazing.