# Fast Diffusion EM: a diffusion model for blind inverse problems with application to deconvolution

arXiv: https://arxiv.org/abs/2309.00287 · HTML: https://mlsanity.com/paper/2309.00287/

## Key facts

- Cited by 36 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 32 of its 57 references that are in the map.
- First posted on arXiv 1 Sep 2023.

## 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 32)

- [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)
- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (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)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [Deblurring via Stochastic Refinement](https://mlsanity.com/paper/2112.02475/) (2021)
- [Learning a Single Convolutional Super-Resolution Network for Multiple Degradations](https://mlsanity.com/paper/1712.06116/) (2017)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Blind Super-Resolution Kernel Estimation using an Internal-GAN](https://mlsanity.com/paper/1909.06581/) (2019)
- [Neural Blind Deconvolution Using Deep Priors](https://mlsanity.com/paper/1908.02197/) (2019)
- [Parallel Diffusion Models of Operator and Image for Blind Inverse Problems](https://mlsanity.com/paper/2211.10656/) (2022)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie](https://mlsanity.com/paper/2103.04715/) (2021)
- [Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging](https://mlsanity.com/paper/2203.17061/) (2022)
- [Flow-based Kernel Prior with Application to Blind Super-Resolution](https://mlsanity.com/paper/2103.15977/) (2021)
- [Deep Constrained Least Squares for Blind Image Super-Resolution](https://mlsanity.com/paper/2202.07508/) (2022)
- [Deep Model-Based Super-Resolution with Non-uniform Blur](https://mlsanity.com/paper/2204.10109/) (2022)

## Built on by (most cited first, 30 of 36)

- [Diffusion Models in Low-Level Vision: A Survey](https://mlsanity.com/paper/2406.11138/) (2024)
- [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)
- [Blind Image Restoration via Fast Diffusion Inversion](https://mlsanity.com/paper/2405.19572/) (2024)
- [Diffusion models for inverse problems](https://mlsanity.com/paper/2508.01975/) (2025)
- [Adaptive Compressed Sensing with Diffusion-Based Posterior Sampling](https://mlsanity.com/paper/2407.08256/) (2024)
- [Unsupervised Blind Joint Dereverberation and Room Acoustics Estimation with Diffusion Models](https://mlsanity.com/paper/2408.07472/) (2024)
- [Blind Inversion using Latent Diffusion Priors](https://mlsanity.com/paper/2407.01027/) (2024)
- [BUDDy: Single-Channel Blind Unsupervised Dereverberation with Diffusion Models](https://mlsanity.com/paper/2405.04272/) (2024)
- [InterLCM: Low-Quality Images as Intermediate States of Latent Consistency Models for Effective Blind Face Restoration](https://mlsanity.com/paper/2502.02215/) (2025)
- [One-Step Diffusion Model for Image Motion-Deblurring](https://mlsanity.com/paper/2503.06537/) (2025)
- [ArrayDPS: Unsupervised Blind Speech Separation with a Diffusion Prior](https://mlsanity.com/paper/2505.05657/) (2025)
- [Do Bayesian imaging methods report trustworthy probabilities?](https://mlsanity.com/paper/2405.08179/) (2024)
- [Empirical Bayesian image restoration by Langevin sampling with a denoising diffusion implicit prior](https://mlsanity.com/paper/2409.04384/) (2024)
- [FLAIR: A Conditional Diffusion Framework with Applications to Face Video Restoration](https://mlsanity.com/paper/2311.15445/) (2023)
- [Listening to the Noise: Blind Denoising with Gibbs Diffusion](https://mlsanity.com/paper/2402.19455/) (2024)
- [Unsupervised Imaging Inverse Problems with Diffusion Distribution Matching](https://mlsanity.com/paper/2506.14605/) (2025)
- [Taming Generative Diffusion Prior for Universal Blind Image Restoration](https://mlsanity.com/paper/2408.11287/) (2024)
- [CryoFM: A Flow-based Foundation Model for Cryo-EM Densities](https://mlsanity.com/paper/2410.08631/) (2024)
- [Unsupervised Estimation of Nonlinear Audio Effects: Comparing Diffusion-Based and Adversarial approaches](https://mlsanity.com/paper/2504.04751/) (2025)
- [DynFaceRestore: Balancing Fidelity and Quality in Diffusion-Guided Blind Face Restoration with Dynamic Blur-Level Mapping and Guidance](https://mlsanity.com/paper/2507.13797/) (2025)
- [Blind Strong Gravitational Lensing Inversion: Joint Inference of Source and Lens Mass with Score-Based Models](https://mlsanity.com/paper/2511.04792/) (2025)
- [Mixed Noise and Posterior Estimation with Conditional DeepGEM](https://mlsanity.com/paper/2402.02964/) (2024)
- [Linearly Constrained Diffusion Implicit Models](https://mlsanity.com/paper/2411.00359/) (2024)
- [Blind Inverse Problem Solving Made Easy by Text-to-Image Latent Diffusion](https://mlsanity.com/paper/2412.00557/) (2024)
- [Double Blind Imaging with Generative Modeling](https://mlsanity.com/paper/2503.21501/) (2025)
- [Position-Blind Ptychography: Viability of image reconstruction via data-driven variational inference](https://mlsanity.com/paper/2509.25269/) (2025)
- [Let Language Constrain Geometry: Vision-Language Models as Semantic and Spatial Critics for 3D Generation](https://mlsanity.com/paper/2511.14271/) (2025)
- [On the Sample Complexity of Learning for Blind Inverse Problems](https://mlsanity.com/paper/2512.23405/) (2025)
- [Prototype Clustered Diffusion Models for Versatile Inverse Problems](https://mlsanity.com/paper/2407.09768/) (2024)

## Abstract (arXiv)

Using diffusion models to solve inverse problems is a growing field of research. Current methods assume the degradation to be known and provide impressive results in terms of restoration quality and diversity. In this work, we leverage the efficiency of those models to jointly estimate the restored image and unknown parameters of the degradation model such as blur kernel. In particular, we designed an algorithm based on the well-known Expectation-Minimization (EM) estimation method and diffusion models. Our method alternates between approximating the expected log-likelihood of the inverse problem using samples drawn from a diffusion model and a maximization step to estimate unknown model parameters. For the maximization step, we also introduce a novel blur kernel regularization based on a Plug & Play denoiser. Diffusion models are long to run, thus we provide a fast version of our algorithm. Extensive experiments on blind image deblurring demonstrate the effectiveness of our method when compared to other state-of-the-art approaches.