The future sixth-generation (6G) of wireless networks is expected to surpass its predecessors by offering ubiquitous coverage through integrated air-ground facility deployments in both communication and computing domains. In this network, aerial facilities, such as unmanned aerial vehicles (UAVs), conduct artificial intelligence (AI) computations based on multi-modal data to support diverse applications including surveillance and environment construction. However, these multi-domain inference and content generation tasks require large AI models, demanding powerful computing capabilities, thus posing significant challenges for UAVs. To tackle this problem, we propose an integrated edge-cloud model evolution framework, where UAVs serve as edge nodes for data collection and edge model computation. Through wireless channels, UAVs collaborate with ground cloud servers, providing cloud model computation and model updating for edge UAVs. With limited wireless communication bandwidth, the proposed framework faces the challenge of information exchange scheduling between the edge UAVs and the cloud server. To tackle this, we present joint task allocation, transmission resource allocation, transmission data quantization design, and edge model update design to enhance the inference accuracy of the integrated air-ground edge-cloud model evolution framework by mean average precision (mAP) maximization. A closed-form lower bound on the mAP of the proposed framework is derived, and the solution to the mAP maximization problem is optimized accordingly. Simulations, based on results from vision-based classification experiments, consistently demonstrate that the mAP of the proposed framework outperforms both a centralized cloud model framework and a distributed edge model framework across various communication bandwidths and data sizes.