Due to the surging amount of AI-generated images, its provisioning to edges and mobile users from the cloud incurs substantial traffic on networks. Generative semantic communication (GSC) offers a promising solution by transmitting highly compact information, i.e., prompt text and latent representations, instead of high-dimensional image data. However, GSC relies on the alignment between the knowledge in the cloud generative AI (GAI) and that possessed by the edges and users, and between the knowledge for wireless transmission and that of actual channels, which remains challenging. In this paper, we propose DeKA-g, a distillation-enabled knowledge alignment algorithm for GSC systems. The core idea is to distill the image generation knowledge from the cloud-GAI into low-rank matrices, which can be incorporated by the edge and used to adapt the transmission knowledge to diverse wireless channel conditions. DeKA-g comprises two novel methods: metaword-aided knowledge distillation (MAKD) and condition-aware low-rank adaptation (CALA). For MAKD, an optimized metaword is employed to enhance the efficiency of knowledge distillation, while CALA enables efficient adaptation to diverse rate requirements and channel conditions. From simulation results, DeKA-g improves the consistency between the edge-generated images and the cloud-generated ones by 44% and enahnces the average transmission quality in terms of PSNR by 6.5 dB over the baselines without knowledge alignment.