ELAD: Blind Face Restoration using Expectation-based Likelihood Approximation and Diffusion Prior

Abstract

Blind Face Restoration (BFR) aims to recover face images suffering from unknown degradations. A recent approach to solve BFR is via plug-and-play methods for image restoration, which combine a likelihood function with pre-trained diffusion models as priors. However, as the likelihood is inherently unknown in BFR, existing methods rely instead on heuristic constraints. This leads to suboptimal distortion and identity preservation metrics. We introduce Expectation-based Likelihood Approximation with Diffusion prior (ELAD), a novel plug-and-play approach that explicitly models the likelihood function for BFR. ELAD estimates the first and second moments of the likelihood distribution by employing a Degradation Estimator to predict the degradation sequence from the input. This enables principled Bayesian inference without requiring end-to-end training. Our method achieves state-of-the-art distortion and identity preservation results compared to existing plug-and-play BFR techniques, while maintaining competitive perceptual quality. As we show, while being plug-and-play, our method still rivals end-to-end trained BFR models.

Problem overview

Real-world blind face restoration observes only a degraded measurement $y$, produced by an unknown sequence of degradations applied to a clean image $x$. Our goal is to sample restored images $\\hat{x}$ that are consistent with the measurements while maintaining high perceptual quality.

(top) A clean image $x$ undergoes a sequence of blur, down-sampling, noising, and compression-decompression operations with unknown parameters $a$ to create the observed degraded measurement $y$. (bottom) Given $y$, we aim to sample images $\hat{x}$ from the posterior $p_{X\mid Y,A}$, each consistent with the measurements and with high perceptual quality.

Plug-and-play Blind Restoration Algorithm

Using the degradation estimator and a pre-trained diffusion model, we construct a blind restoration algorithm. We extend prior P&P algorithms such as DPS to support more general degradations (where the noise is not the last operation) by approximating the likelihood using its first-moment.

Degradation Estimation

Degradation estimator

We train a degradation estimator that predicts the parameters of the degradations applied to an image. The estimator achieves high accuracy on blind face degradations, as seen visually from the scatter plots and quantitatively from the R-squared scores.

Degradations in real-world BFR datasets

Using our degradation estimator, we reveal the degradations’ distribution in real-world datasets. This information can be utilized to better analyze such datasets and mimic them.

Proxy MSE & LPIPS

Given a pre-trained MMSE regressor (an $L_2$ trained NN), we show how to construct a no-reference distortion measure that mimics the ubiquitous MSE measure. Moreover, by training a simple LPIPS regressor, we construct a similar no-reference measure that mimics LPIPS. Using those measures, we can, for the first time, test the distortion performance of restoration algorithms with no need to access ground-truth data, which is typically unavailable in real-world blind settings.

BibTeX citation

@inproceedings{10.1145/3757377.3763969,
author = {Man, Sean and Ohayon, Guy and Raphaeli, Ron and Kleiner, Matan and Elad, Michael},
title = {ELAD: Blind Face Restoration using Expectation-based Likelihood Approximation and Diffusion Prior},
year = {2025},
isbn = {9798400721373},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3757377.3763969},
doi = {10.1145/3757377.3763969},
booktitle = {Proceedings of the SIGGRAPH Asia 2025 Conference Papers},
articleno = {63},
numpages = {12},
keywords = {Blind Face Restoration, Image Restoration, Plug and Play, Diffusion Prior, Posterior Sampling},
location = {
},
series = {SA Conference Papers '25}
}