With the continuous development of globalization and customization demands, the distributed assembly flowshop scheduling problem (DAFSP) has received widespread attention. To add the practicality, this paper further considers the constraints of fuzzy processing time and production deadlock caused by finite assembly buffer in the DAFSP, and therefore a novel fuzzy distributed assembly flowshop deadlock-free scheduling problem (FDAFDSP) is studied. To address this problem, the calculational model is first developed to minimize the maximum fuzzy completion time. Secondly, a Petri nets-based deadlock detection and repair algorithm is proposed to avoid system deadlock. Then, based on deadlock avoidance algorithms and generative adversarial networks (GANs), a GANs-based deadlock-free scheduling algorithm (GAN-DSA) is established for the FDAFDSP, which can avoid deadlocks and achieve efficient scheduling. Finally, the effectiveness of the GAN-DSA for solving the FDAFDSP is experimentally validated by comparing it with related algorithms on 32 test instances.