## 1 Introduction  
For decades, rate-distortion (RD) theory has served as the de facto standard for evaluating real-world applications involving compression and communication. With the advances in artificial intelligence technologies, the dimension of perceptual fidelity has been increasingly recognized as a crucial aspect. While traditional distortion measures like mean squared error (MSE) have served well in many applications, they fail to capture the perceptual quality that humans actually experience [1, 2, 3]. This disconnect has motivated the integration of perceptual measures into RD, leading to the emergence of the rate-distortion-perception (RDP) framework [4]. The information RDP function incorporates an additional perceptual constraint measured by the divergence between the input and reconstruction distributions within the context of lossy compression using machine learning. Unlike conventional distortion measures, perceptual fidelity captures the global properties of the entire coding block rather than focusing on individual sample positions,giving rise to new coding theorems. Consequently, RD plots, which have long been used to evaluate practical source coding algorithms, should be updated to incorporate this new dimension in alignment with the emerging coding theorems (see Figure 1b,c for a comparison of the RDP frontier with the RD curves). This development has also inspired a variety of innovative source coding methods that rely on generative models [5; 6; 7; 8; 9; 10; 11]. As emerging techniques are increasingly applied to lossy source coding and communication systems in general, the RDP trade-off offers a novel perspective for evaluating the performance of machine-learning-aided systems. Recent advances in AI-empowered communication have reimagined communication systems as a joint optimization of transmitter and receiver through end-to-end training for reconstruction tasks [12; 13]. Therefore, in communication systems where downstream tasks demand high perceptual fidelity, such as interactive AI agents and the reconstruction of visually pleasing content, the RDP framework is particularly useful. This paper explores the critical role of perceptual constraints in information theory and their impact on practical generative modeling scenarios, which drives the development of a wide range of compression and communication algorithms that integrate various generative model architectures with end-to-end training objectives. We demonstrate how incorporating perceptual constraints into the traditional RD framework offers a comprehensive perspective for evaluating the performance of AI-empowered systems in communication and potentially increases network traffic. The capacity to perceive, communicate, and learn from the environment, as well as to construct mental models that internally simulate potential outcomes, is fundamental to both human and artificial intelligence. In early neuroscience research, perception was conceptualized as a form of hypothesis testing [16], a notion that naturally aligns with the divergence measure for perceptual quality in information theory. More recently, the theory of predictive coding has posited that generative models of the world are derived from sensory input, perception being understood as the minimization of prediction errors [17; 18]. Developing models capable of mimicking human-like perception and reasoning, including visual aesthetics and consistency; language perplexity and fluency, among others, is essential for the creation of useful generative models. Contemporary large language models (LLMs) and multi-modal models have demonstrated remarkable capabilities, such as memorization [19], generation of images and videos based on descriptive prompts [20], retrieval and reasoning [21]. During the training of these generative models, the loss function typi  
Figure 1: Rate–distortion–perception trade-off. **(a)** Rate–distortion curves with and without the realism constraint for a Gaussian source.