Reasons for the Superiority of Stochastic Estimators over Deterministic Ones: Robustness, Consistency and Perceptual Quality

TL;DR

This paper demonstrates that stochastic restoration algorithms have fundamental advantages over deterministic ones, including robustness, consistency, and the ability to achieve high perceptual quality without vulnerability to adversarial attacks.

Contribution

It proves that perfect perceptual quality with consistency requires stochastic methods and shows stochastic models are more robust and versatile than deterministic ones.

Findings

Stochastic methods are necessary for perfect perceptual quality with consistency.

Deterministic algorithms are more vulnerable to adversarial attacks.

Robust stochastic models maintain perceptual quality and output variability.

Abstract

Stochastic restoration algorithms allow to explore the space of solutions that correspond to the degraded input. In this paper we reveal additional fundamental advantages of stochastic methods over deterministic ones, which further motivate their use. First, we prove that any restoration algorithm that attains perfect perceptual quality and whose outputs are consistent with the input must be a posterior sampler, and is thus required to be stochastic. Second, we illustrate that while deterministic restoration algorithms may attain high perceptual quality, this can be achieved only by filling up the space of all possible source images using an extremely sensitive mapping, which makes them highly vulnerable to adversarial attacks. Indeed, we show that enforcing deterministic models to be robust to such attacks profoundly hinders their perceptual quality, while robustifying stochastic models hardly influences their perceptual quality, and improves their output variability. These findings provide a motivation to foster progress in stochastic restoration methods, paving the way to better recovery algorithms.