  The pursuit of high perceptual quality in image restoration has driven the
development of revolutionary generative models, capable of producing results
often visually indistinguishable from real data. However, as their perceptual
quality continues to improve, these models also exhibit a growing tendency to
generate hallucinations - realistic-looking details that do not exist in the
ground truth images. The presence of hallucinations introduces uncertainty
regarding the reliability of the models' predictions, raising major concerns
about their practical application. In this paper, we employ information-theory
tools to investigate this phenomenon, revealing a fundamental tradeoff between
uncertainty and perception. We rigorously analyze the relationship between
these two factors, proving that the global minimal uncertainty in generative
models grows in tandem with perception. In particular, we define the inherent
uncertainty of the restoration problem and show that attaining perfect
perceptual quality entails at least twice this uncertainty. Additionally, we
establish a relation between mean squared-error distortion, uncertainty and
perception, through which we prove the aforementioned uncertainly-perception
tradeoff induces the well-known perception-distortion tradeoff. This work
uncovers fundamental limitations of generative models in achieving both high
perceptual quality and reliable predictions for image restoration. We
demonstrate our theoretical findings through an analysis of single image
super-resolution algorithms. Our work aims to raise awareness among
practitioners about this inherent tradeoff, empowering them to make informed
decisions and potentially prioritize safety over perceptual performance.
