The sixth-generation (6G) of wireless networks is expected to surpass its predecessors by offering ubiquitous coverage of sensing, communication, and computing by the deployment of space-air-ground integrated networks (SAGINs). In SAGINs, aerial facilities, such as unmanned aerial vehicles (UAVs), collect multi-modal sensory data to support diverse applications including surveillance and battlefield monitoring. However, these processing of the multi-domain inference tasks require large artificial intelligence (AI) models, demanding powerful computing capabilities and finely tuned inference models trained on rich datasets, thus posing significant challenges for UAVs. To provide ubiquitous powerful computation, we propose a SAGIN model collaboration framework, where LEO satellites with ubiquitous service coverage and ground servers with powerful computing capabilities work as edge nodes and cloud nodes, respectively, for the processing of sensory data from the UAVs. With limited communication bandwidth and computing capacity, the proposed framework faces the challenge of computing allocation among the edge nodes and the cloud nodes, together with the uplink-downlink resource allocation for the sensory data and model transmissions. To tackle this, we present joint edge-cloud task allocation, air-space-ground communication resource allocation, and sensory data quantization design to maximize the inference accuracy of the SAGIN model collaboration framework. The mixed integer programming problem is decomposed into two subproblems, and solved based on the propositions summarized from experimental studies. Simulations based on results from vision-based classification experiments consistently demonstrate that the inference accuracy of the SAGIN model collaboration framework outperforms both a centralized cloud model framework and a distributed edge model framework across various communication bandwidths and data sizes.