# Unleashing the Denoising Capability of Diffusion Prior for Solving Inverse Problems

arXiv: https://arxiv.org/abs/2406.06959 · HTML: https://mlsanity.com/paper/2406.06959/

## Key facts

- Cited by 7 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 58 references that are in the map.
- First posted on arXiv 11 Jun 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 30)

- [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)
- [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)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Colorful Image Colorization](https://mlsanity.com/paper/1603.08511/) (2016)
- [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)
- [SDR - half-baked or well done?](https://mlsanity.com/paper/1811.02508/) (2018)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [Solving 3D Inverse Problems using Pre-trained 2D Diffusion Models](https://mlsanity.com/paper/2211.10655/) (2022)
- [Cutting Music Source Separation Some Slakh: A Dataset to Study the Impact of Training Data Quality and Quantity](https://mlsanity.com/paper/1909.08494/) (2019)
- [Multi-Source Diffusion Models for Simultaneous Music Generation and Separation](https://mlsanity.com/paper/2302.02257/) (2023)
- [Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems](https://mlsanity.com/paper/2211.12343/) (2022)
- [Generalized Multi-Source Inference for Text Conditioned Music Diffusion Models](https://mlsanity.com/paper/2403.11706/) (2024)
- [Improving Source Separation by Explicitly Modeling Dependencies Between Sources](https://mlsanity.com/paper/2203.15140/) (2022)

## Built on by (most cited first, 7 of 7)

- [Angle Domain Guidance: Latent Diffusion Requires Rotation Rather Than Extrapolation](https://mlsanity.com/paper/2506.11039/) (2025)
- [Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2505.20789/) (2025)
- [Improving Diffusion-based Inverse Algorithms under Few-Step Constraint via Learnable Linear Extrapolation](https://mlsanity.com/paper/2503.10103/) (2025)
- [Provable diffusion-based posterior sampling for linear inverse problems via DDIM](https://mlsanity.com/paper/2607.19333/) (2026)
- [Coupled Data and Measurement Space Dynamics for Enhanced Diffusion Posterior Sampling](https://mlsanity.com/paper/2510.09676/) (2025)
- [Image Restoration via Diffusion Models with Dynamic Resolution](https://mlsanity.com/paper/2605.14267/) (2026)
- [Tracing the Oracle: Improving Diffusion Timestep Scheduling for 3D CT Reconstruction](https://mlsanity.com/paper/2606.06236/) (2026)

## Abstract (arXiv)

The recent emergence of diffusion models has significantly advanced the precision of learnable priors, presenting innovative avenues for addressing inverse problems. Since inverse problems inherently entail maximum a posteriori estimation, previous works have endeavored to integrate diffusion priors into the optimization frameworks. However, prevailing optimization-based inverse algorithms primarily exploit the prior information within the diffusion models while neglecting their denoising capability. To bridge this gap, this work leverages the diffusion process to reframe noisy inverse problems as a two-variable constrained optimization task by introducing an auxiliary optimization variable. By employing gradient truncation, the projection gradient descent method is efficiently utilized to solve the corresponding optimization problem. The proposed algorithm, termed ProjDiff, effectively harnesses the prior information and the denoising capability of a pre-trained diffusion model within the optimization framework. Extensive experiments on the image restoration tasks and source separation and partial generation tasks demonstrate that ProjDiff exhibits superior performance across various linear and nonlinear inverse problems, highlighting its potential for practical applications. Code is available at https://github.com/weigerzan/ProjDiff/.