Looks Too Good To Be True: An Information-Theoretic Analysis of Hallucinations in Generative Restoration Models

TL;DR

This work defines the inherent uncertainty of the restoration problem and shows that attaining perfect perceptual quality entails at least twice this uncertainty, and establishes a relation between distortion, uncertainty and perception, through which it is proved the aforementioned uncertainly-perception tradeoff induces the well-known perception-distortion tradeoff.

Abstract

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. Hallucinations in these models create uncertainty about their reliability, raising major concerns about their practical application. This paper investigates this phenomenon through the lens of information theory, 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 distortion, uncertainty and perception, through which we prove the aforementioned uncertainly-perception tradeoff induces the well-known perception-distortion tradeoff. We demonstrate our theoretical findings through experiments with super-resolution and inpainting algorithms. This work uncovers fundamental limitations of generative models in achieving both high perceptual quality and reliable predictions for image restoration. Thus, we aim to raise awareness among practitioners about this inherent tradeoff, empowering them to make informed decisions and potentially prioritize safety over perceptual performance.

Figures (7)

• Figure 2: Image inpainting results. Algorithms are ordered from low to high perception (left to right). Note the corresponding increased hallucinations and distortion. See Section \ref{['sec:exp']} for details.
• Figure 3: The uncertainty-perception plane (Theorem \ref{['thm:renyi']}). The impossible region demonstrates the inherent tradeoff between perception and uncertainty, while other regions may guide practitioners toward estimators that better balance the two factors, highlighting potential areas for improvement.
• Figure 4: Impact of dimensionality, as revealed in Theorem \ref{['thm:renyi']}, demonstrates that the uncertainty-perception tradeoff intensifies in higher dimensions. This implies that even minor improvements in perceptual quality for an algorithm may come at the cost of a significant increase in uncertainty.
• Figure 5: Evaluation of SR algorithms. Top: Uncertainty-perception plane showing the tradeoff between perceptual quality and uncertainty (y-axis) for various perceptual measures. Bottom: Uncertainty-distortion plane showing the relationship between uncertainty and various distortion measures. Axis placement differs in the two rows to highlight the distinct roles of uncertainty.
• Figure 6: Evaluation of LDMs on image inpainting, highlighting the trade-off between uncertainty and perceptual quality (top) and the uncertainty-distortion relationship (bottom). No model achieves both low uncertainty and high perceptual quality, with higher uncertainty generally leading to increased distortion. Differing axis placements emphasize the distinct roles of uncertainty.

Theorems & Definitions (16)

• Definition 1
• Definition 2
• Example 1
• Theorem 1
• Theorem 2
• Theorem 3
• Theorem 4
• Corollary 1
• Definition 3: Entropy
• Definition 4: Rényi Entropy