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

Understand

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.