Agentic Satellite-Augmented Low-Altitude Economy and Terrestrial Networks: A Survey on Generative Approaches

The development of satellite-augmented low-altitude economy and terrestrial networks (SLAETNs) demands intelligent and autonomous systems that can operate reliably across heterogeneous, dynamic, and mission-critical environments. To address these challenges, this survey focuses on enabling agentic artificial intelligence (AI), that is, artificial agents capable of perceiving, reasoning, and acting, through generative AI (GAI) and large language models (LLMs). We begin by introducing the architecture and characteristics of SLAETNs, and analyzing the challenges that arise in integrating satellite, aerial, and terrestrial components. Then, we present a model-driven foundation by systematically reviewing five major categories of generative models: variational autoencoders (VAEs), generative adversarial networks (GANs), generative diffusion models (GDMs), transformer-based models (TBMs), and LLMs. Moreover, we provide a comparative analysis to highlight their generative mechanisms, capabilities, and deployment trade-offs within SLAETNs. Building on this foundation, we examine how these models empower agentic functions across three domains: communication enhancement, security and privacy protection, and intelligent satellite tasks. Finally, we outline key future directions for building scalable, adaptive, and trustworthy generative agents in SLAETNs. This survey aims to provide a unified understanding and actionable reference for advancing agentic AI in next-generation integrated networks.