In distributed inference, local cooperation among network nodes can be exploited to enhance the performance of each individual agent, but a challenging requirement for networks operating in dynamic real-world environments is that of adaptation. The interplay between these two fundamental aspects of cooperation and adaptation has been investigated in recent years in the context of estimation problems. Less explored in the literature is the case of detection, which is our focus. Capitalizing on the powerful tool of large deviations analysis, we show how to design and characterize the performance of diffusion strategies that reconcile both needs of adaptation and detection in decentralized systems.