Generative models have achieved remarkable performance in restoration tasks, producing results nearly indistinguishable from real data. However, they are prone to generating artifacts or hallucinations not present in the original input, inducing estimation uncertainty. Notably, the extent of hallucination seems to increase with the perceptual quality of the generative model. This paper explores this phenomenon using information-theoretic tools to uncover an inherent tradeoff between perception and uncertainty. Our mathematical analysis shows that the uncertainty of the restoration algorithm, as measured by error entropy, grows in tandem with the improvement in perceptual quality. Employing R'enyi divergence as a perception measure, we derive lower and upper bounds for the tradeoff, locating estimators into distinct performance categories. Furthermore, we establish a relationship between estimation distortion and uncertainty, through which we provide a fresh perspective on the perception-distortion tradeoff. Our work presents a principled analysis of uncertainty, emphasizing its interplay with perception and distortion, and the limitations of generative models in restoration tasks.