  Recently, generative AI technologies have emerged as a significant
advancement in artificial intelligence field, renowned for their language and
image generation capabilities. Meantime, space-air-ground integrated network
(SAGIN) is an integral part of future B5G/6G for achieving ubiquitous
connectivity. Inspired by this, this article explores an integration of
generative AI in SAGIN, focusing on potential applications and case study. We
first provide a comprehensive review of SAGIN and generative AI models,
highlighting their capabilities and opportunities of their integration.
Benefiting from generative AI's ability to generate useful data and facilitate
advanced decision-making processes, it can be applied to various scenarios of
SAGIN. Accordingly, we present a concise survey on their integration, including
channel modeling and channel state information (CSI) estimation, joint
air-space-ground resource allocation, intelligent network deployment, semantic
communications, image extraction and processing, security and privacy
enhancement. Next, we propose a framework that utilizes a Generative Diffusion
Model (GDM) to construct channel information map to enhance quality of service
for SAGIN. Simulation results demonstrate the effectiveness of the proposed
framework. Finally, we discuss potential research directions for generative
AI-enabled SAGIN.
