This article targets at unlocking the potentials of a class of prominent generative artificial intelligence (GAI) method, namely diffusion model (DM), for mobile communications. First, a DM-driven communication architecture is proposed, which introduces two key paradigms, i.e., conditional DM and DM-driven deep reinforcement learning (DRL), for wireless data generation and communication management, respectively. Then, we discuss the key advantages of DM-driven communication paradigms. To elaborate further, we explore DM-driven channel generation mechanisms for channel estimation, extrapolation, and feedback in multiple-input multiple-output (MIMO) systems. We showcase the numerical performance of conditional DM using the accurate DeepMIMO channel datasets, revealing its superiority in generating high-fidelity channels and mitigating unforeseen distribution shifts in sophisticated scenes. Furthermore, several DM-driven communication management designs are conceived, which is promising to deal with imperfect channels and task-oriented communications. To inspire future research developments, we highlight the potential applications and open research challenges of DM-driven communications. Code is available at https://github.com/xiaoxiaxusummer/GAI_COMM/