Data augmentation is a powerful technique to mitigate data scarcity. However, owing to fundamental differences in wireless data structures, traditional data augmentation techniques may not be suitable for wireless data. Fortunately, Generative Artificial Intelligence (GenAI) can be an effective alternative to wireless data augmentation due to its excellent data generation capability. This article systemically explores the potential and effectiveness of GenAI-driven data augmentation in wireless networks. We first briefly review data augmentation techniques, discuss their limitations in wireless networks, and introduce generative data augmentation, including reviewing GenAI models and their applications in data augmentation. We then explore the application prospects of GenAI-driven data augmentation in wireless networks from the physical, network, and application layers, which provides a GenAI-driven data augmentation architecture for each application. Subsequently, we propose a general generative diffusion model-based data augmentation framework for Wi-Fi gesture recognition, which uses transformer-based diffusion models to generate high-quality channel state information data. Furthermore, we develop residual neural network models for Wi-Fi gesture recognition to evaluate the role of augmented data and conduct a case study based on a real dataset. Simulation results demonstrate the effectiveness of the proposed framework. Finally, we discuss research directions for generative data augmentation.