# Solving Inverse Problems using Diffusion with Iterative Colored Renoising

arXiv: https://arxiv.org/abs/2501.17468 · HTML: https://mlsanity.com/paper/2501.17468/

## 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 30 of its 51 references that are in the map.
- First posted on arXiv 29 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 30)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [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)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [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)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing](https://mlsanity.com/paper/2407.01521/) (2024)
- [The probability flow ODE is provably fast](https://mlsanity.com/paper/2305.11798/) (2023)
- [Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems](https://mlsanity.com/paper/2303.05754/) (2023)
- [Regularization by Denoising: Clarifications and New Interpretations](https://mlsanity.com/paper/1806.02296/) (2018)
- [Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie](https://mlsanity.com/paper/2103.04715/) (2021)
- [Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors](https://mlsanity.com/paper/2405.18782/) (2024)
- [Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction](https://mlsanity.com/paper/2403.17042/) (2024)
- [Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inference](https://mlsanity.com/paper/2304.11134/) (2023)
- [Phase Retrieval from Coded Diffraction Patterns](https://mlsanity.com/paper/1310.3240/) (2013)
- [Generative Plug and Play: Posterior Sampling for Inverse Problems](https://mlsanity.com/paper/2306.07233/) (2023)
- [Plug-and-Play image restoration with Stochastic deNOising REgularization](https://mlsanity.com/paper/2402.01779/) (2024)

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

- [Plug-and-Play Diffusion Meets ADMM: Dual-Variable Coupling for Robust Medical Image Reconstruction](https://mlsanity.com/paper/2602.23214/) (2026)

## Abstract (arXiv)

Imaging inverse problems can be solved in an unsupervised manner using pre-trained diffusion models, but doing so requires approximating the gradient of the measurement-conditional score function in the diffusion reverse process. We show that the approximations produced by existing methods are relatively poor, especially early in the reverse process, and so we propose a new approach that iteratively reestimates and "renoises" the estimate several times per diffusion step. This iterative approach, which we call Fast Iterative REnoising (FIRE), injects colored noise that is shaped to ensure that the pre-trained diffusion model always sees white noise, in accordance with how it was trained. We then embed FIRE into the DDIM reverse process and show that the resulting "DDfire" offers state-of-the-art accuracy and runtime on several linear inverse problems, as well as phase retrieval. Our implementation is at https://github.com/matt-bendel/DDfire