The rapid advancement of 6G wireless networks, IoT, and edge computing has significantly expanded the cyberattack surface, necessitating more intelligent and adaptive vulnerability detection mechanisms. Traditional security methods, while foundational, struggle with zero-day exploits, adversarial threats, and context-dependent vulnerabilities in highly dynamic network environments. Generative AI (GAI) emerges as a transformative solution, leveraging synthetic data generation, multimodal reasoning, and adaptive learning to enhance security frameworks. This paper explores the integration of GAI-powered vulnerability detection in 6G wireless networks, focusing on code auditing, protocol security, cloud-edge defenses, and hardware protection. We introduce a three-layer framework comprising the Technology Layer, Capability Layer, and Application Layer to systematically analyze the role of VAEs, GANs, LLMs, and GDMs in securing next-generation wireless ecosystems. To demonstrate practical implementation, we present a case study on LLM-driven code vulnerability detection, highlighting its effectiveness, performance, and challenges. Finally, we outline future research directions, including lightweight models, high-authenticity data generation, external knowledge integration, and privacy-preserving technologies. By synthesizing current advancements and open challenges, this work provides a roadmap for researchers and practitioners to harness GAI for building resilient and adaptive security solutions in 6G networks.