In wireless networks, applying deep learning models to solve matching problems between different entities has become a mainstream and effective approach. However, the complex network topology in 6G multiple access presents significant challenges for the real-time performance and stability of matching generation. Generative artificial intelligence (GenAI) has demonstrated strong capabilities in graph feature extraction, exploration, and generation, offering potential for graph-structured matching generation. In this paper, we propose a GenAI-enabled matching generation framework to support 6G multiple access. Specifically, we first summarize the classical matching theory, discuss common GenAI models and applications from the perspective of matching generation. Then, we propose a framework based on generative diffusion models (GDMs) that iteratively denoises toward reward maximization to generate a matching strategy that meets specific requirements. Experimental results show that, compared to decision-based AI approaches, our framework can generate more effective matching strategies based on given conditions and predefined rewards, helping to solve complex problems in 6G multiple access, such as task allocation.