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.

翻译：在图像修复领域追求高感知质量的过程中，革命性的生成模型得以发展，其生成结果在视觉上常与真实数据难以区分。然而，随着其感知质量的持续提升，这些模型也表现出日益增长的幻觉生成倾向——即生成在视觉上逼真但实际在真实图像中并不存在的细节。幻觉的存在引入了关于模型预测可靠性的不确定性，对其实际应用提出了重大关切。本文运用信息论工具研究这一现象，揭示了不确定性与感知之间的根本性权衡。我们严格分析了这两个因素之间的关系，证明了生成模型中的全局最小不确定性会随着感知质量的提升而同步增长。具体而言，我们定义了修复问题的固有不确定性，并证明要达到完美的感知质量至少需要承担两倍于此的不确定性。此外，我们通过建立均方误差失真、不确定性与感知之间的关系，证明了上述不确定性-感知权衡导致了众所周知的感知-失真权衡。这项工作揭示了生成模型在图像修复任务中同时实现高感知质量与可靠预测的根本性局限。我们通过对单图像超分辨率算法的分析验证了理论发现。本研究旨在提高实践者对此固有权衡的认识，使其能够做出明智的决策，并可能在感知性能与安全性之间优先考虑后者。