Computerized Adaptive Testing (CAT) measures student ability by iteratively selecting informative questions, with core components being the Cognitive Diagnosis Model (CDM) and selection strategy. Current research focuses on optimizing the selection strategy, assuming relatively accurate CDM results. However, existing static CDMs struggle with rapid and accurate diagnosis in the early stage of CAT. To this end, this paper proposes a Fast Adaptive Cognitive Diagnosis (FACD) framework, which incorporates dynamic collaborative and personalized diagnosis modules. Specifically, the collaborative module in FACD uses a dynamic response graph to quickly build student cognitive profiles, while the personalized module leverages each student's response sequence for robust and individualized diagnosis. Extensive experiments on real-world datasets show that, compared with existing static CDMs, FACD not only achieves superior prediction performance across various selection strategies with an improvement between roughly 5%-10% in the early stage of CAT, but also maintains a commendable inference speed.