  As the next-generation wireless communication system, Sixth-Generation (6G)
technologies are emerging, enabling various mobile edge networks that can
revolutionize wireless communication and connectivity. By integrating
Generative Artificial Intelligence (GAI) with mobile edge networks, generative
mobile edge networks possess immense potential to enhance the intelligence and
efficiency of wireless communication networks. In this article, we propose the
concept of generative mobile edge networks and overview widely adopted GAI
technologies and their applications in mobile edge networks. We then discuss
the potential challenges faced by generative mobile edge networks in
resource-constrained scenarios. To address these challenges, we develop a
universal resource-efficient generative incentive mechanism framework, in which
we design resource-efficient methods for network overhead reduction, formulate
appropriate incentive mechanisms for the resource allocation problem, and
utilize Generative Diffusion Models (GDMs) to find the optimal incentive
mechanism solutions. Furthermore, we conduct a case study on
resource-constrained mobile edge networks, employing model partition for
efficient AI task offloading and proposing a GDM-based Stackelberg model to
motivate edge devices to contribute computing resources for mobile edge
intelligence. Finally, we propose several open directions that could contribute
to the future popularity of generative mobile edge networks.
