Posterior-Mean Rectified Flow (PMRF) is a novel photo-realistic image restoration algorithm. It (provably) approximates the optimal estimator that minimizes the Mean Squared Error (MSE) under a perfect perceptual quality constraint.

We propose a new definition of fairness for image restoration algorithms, draw its connection to previous ones, study its theoretical properties, and demonstrate its practical utility.

We prove that the Lipschitz constant of a deterministic restoration algorithm grows to infinity as the algorithm approaches perfect perceptual quality and perfect consistency with the measurements.

We propose an image restoration algorithm that can control the perceptual quality and/or the mean square error (MSE) of any pre-trained model, trading one over the other at test time.

We propose a novel JPEG decoding GAN-based algorithm that samples from the posterior distribution

We reveal fundamental advantages of stochastic image restoration algorithms over deterministic ones.

We propose a novel CGAN algorithm that avoids the mode collapse issue and samples from the posterior distribution