# Parallel Diffusion Models of Operator and Image for Blind Inverse Problems

arXiv: https://arxiv.org/abs/2211.10656 · HTML: https://mlsanity.com/paper/2211.10656/

## Key facts

- Cited by 113 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 31 of its 64 references that are in the map.
- First posted on arXiv 19 Nov 2022.

## 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 31)

- [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)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [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)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Pre-Trained Image Processing Transformer](https://mlsanity.com/paper/2012.00364/) (2020)
- [Uformer: A General U-Shaped Transformer for Image Restoration](https://mlsanity.com/paper/2106.03106/) (2021)
- [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [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)
- [DeblurGAN: Blind Motion Deblurring Using Conditional Adversarial Networks](https://mlsanity.com/paper/1711.07064/) (2017)
- [DeblurGAN-v2: Deblurring (Orders-of-Magnitude) Faster and Better](https://mlsanity.com/paper/1908.03826/) (2019)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Learning a Convolutional Neural Network for Non-uniform Motion Blur Removal](https://mlsanity.com/paper/1503.00593/) (2015)
- [Neural Blind Deconvolution Using Deep Priors](https://mlsanity.com/paper/1908.02197/) (2019)
- [Learning to Deblur](https://mlsanity.com/paper/1406.7444/) (2014)
- [JPEG Artifact Correction using Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2209.11888/) (2022)
- [Single Frame Atmospheric Turbulence Mitigation: A Benchmark Study and A New Physics-Inspired Transformer Model](https://mlsanity.com/paper/2207.10040/) (2022)
- [Image Reconstruction of Static and Dynamic Scenes through Anisoplanatic Turbulence](https://mlsanity.com/paper/2009.00071/) (2020)
- [Subsampled Turbulence Removal Network](https://mlsanity.com/paper/1807.04418/) (2018)
- [Tilt-then-Blur or Blur-then-Tilt? Clarifying the Atmospheric Turbulence Model](https://mlsanity.com/paper/2207.06377/) (2022)
- [Learning a Discriminative Prior for Blind Image Deblurring](https://mlsanity.com/paper/1803.03363/) (2018)

## Built on by (most cited first, 30 of 113)

- [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)
- [Diffusion Models for Image Restoration and Enhancement: A Comprehensive Survey](https://mlsanity.com/paper/2308.09388/) (2023)
- [Training-free Linear Image Inverses via Flows](https://mlsanity.com/paper/2310.04432/) (2023)
- [Prompt-tuning latent diffusion models for inverse problems](https://mlsanity.com/paper/2310.01110/) (2023)
- [Residual Denoising Diffusion Models](https://mlsanity.com/paper/2308.13712/) (2023)
- [DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2405.16749/) (2024)
- [GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration](https://mlsanity.com/paper/2301.12686/) (2023)
- [Improving 3D Imaging with Pre-Trained Perpendicular 2D Diffusion Models](https://mlsanity.com/paper/2303.08440/) (2023)
- [How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Framework](https://mlsanity.com/paper/2410.03601/) (2024)
- [WaveDM: Wavelet-Based Diffusion Models for Image Restoration](https://mlsanity.com/paper/2305.13819/) (2023)
- [Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithms](https://mlsanity.com/paper/2502.00234/) (2025)
- [Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexity](https://mlsanity.com/paper/2405.15986/) (2024)
- [Image Restoration Through Generalized Ornstein-Uhlenbeck Bridge](https://mlsanity.com/paper/2312.10299/) (2023)
- [Steering Rectified Flow Models in the Vector Field for Controlled Image Generation](https://mlsanity.com/paper/2412.00100/) (2024)
- [Fast Diffusion EM: a diffusion model for blind inverse problems with application to deconvolution](https://mlsanity.com/paper/2309.00287/) (2023)
- [Regularization by Texts for Latent Diffusion Inverse Solvers](https://mlsanity.com/paper/2311.15658/) (2023)
- [Blind Image Restoration via Fast Diffusion Inversion](https://mlsanity.com/paper/2405.19572/) (2024)
- [Token Caching for Diffusion Transformer Acceleration](https://mlsanity.com/paper/2409.18523/) (2024)
- [Conditional Image Synthesis with Diffusion Models: A Survey](https://mlsanity.com/paper/2409.19365/) (2024)
- [Physics-Driven Turbulence Image Restoration with Stochastic Refinement](https://mlsanity.com/paper/2307.10603/) (2023)
- [SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems](https://mlsanity.com/paper/2410.04479/) (2024)
- [Controllable Inversion of Black-Box Face Recognition Models via Diffusion](https://mlsanity.com/paper/2303.13006/) (2023)
- [Accelerating Diffusion Models for Inverse Problems through Shortcut Sampling](https://mlsanity.com/paper/2305.16965/) (2023)
- [Blind Audio Bandwidth Extension: A Diffusion-Based Zero-Shot Approach](https://mlsanity.com/paper/2306.01433/) (2023)
- [Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problems](https://mlsanity.com/paper/2409.20175/) (2024)
- [Diffusion models for inverse problems](https://mlsanity.com/paper/2508.01975/) (2025)
- [Residual Diffusion Bridge Model for Image Restoration](https://mlsanity.com/paper/2510.23116/) (2025)
- [Osmosis: RGBD Diffusion Prior for Underwater Image Restoration](https://mlsanity.com/paper/2403.14837/) (2024)
- [Adaptive Compressed Sensing with Diffusion-Based Posterior Sampling](https://mlsanity.com/paper/2407.08256/) (2024)

## Abstract (arXiv)

Diffusion model-based inverse problem solvers have demonstrated state-of-the-art performance in cases where the forward operator is known (i.e. non-blind). However, the applicability of the method to blind inverse problems has yet to be explored. In this work, we show that we can indeed solve a family of blind inverse problems by constructing another diffusion prior for the forward operator. Specifically, parallel reverse diffusion guided by gradients from the intermediate stages enables joint optimization of both the forward operator parameters as well as the image, such that both are jointly estimated at the end of the parallel reverse diffusion procedure. We show the efficacy of our method on two representative tasks -- blind deblurring, and imaging through turbulence -- and show that our method yields state-of-the-art performance, while also being flexible to be applicable to general blind inverse problems when we know the functional forms.