The high-performance generative artificial intelligence (GAI) represents the latest evolution of computational intelligence, while the blessing of future 6G networks also makes edge intelligence (EI) full of development potential. The inevitable encounter between GAI and EI can unleash new opportunities, where GAI's pre-training based on massive computing resources and large-scale unlabeled corpora can provide strong foundational knowledge for EI, while EI can harness fragmented computing resources to aggregate personalized knowledge for GAI. However, the natural contradictory features pose significant challenges to direct knowledge sharing. To address this, in this paper, we propose the GAI-oriented synthetical network (GaisNet), a collaborative cloud-edge-end intelligence framework that buffers contradiction leveraging data-free knowledge relay, where the bidirectional knowledge flow enables GAI's virtuous-cycle model fine-tuning and task inference, achieving mutualism between GAI and EI with seamless fusion and collaborative evolution. Experimental results demonstrate the effectiveness of the proposed mechanisms. Finally, we discuss the future challenges and directions in the interplay between GAI and EI.