In frequency division duplexing (FDD) systems, the uplink and downlink transmit information in different frequency bands, so it is difficult to use channel reciprocity to generate secret keys. Existing key generation methods for FDD systems have excessive overhead and security problems. This paper uses deep learning to predict the downlink channel state information (CSI) from the uplink CSI, so that two users can generate highly similar downlink CSI in FDD systems. We propose a key generation scheme based on boundary equilibrium generative adversarial network (BEGAN), including channel estimation, reciprocal channel feature construction, quantization, information reconciliation and privacy amplification. Numerical simulation results are presented to verify the feasibility and effectiveness of the proposed scheme.