Distributed cloud systems bring new experiences to various cloud platform-based intelligent applications. Compared with traditional centralized cloud services, they give a greater network performance and lower service latency. However, the complexity of network structure and the diversity of IoT devices pose higher requirements for device authentication in distributed cloud systems. For example, shorter latency in the network demands more efficient authentication schemes, and the diversity of devices requires a unified authentication method between devices and servers. In this article, we propose a cloud-edge-device collaborative device authentication framework based on Physical Unclonable Function (PUF). Given the diverse types of devices, we propose to build a PUF using the components in the device, then model the PUF with machine learning algorithms, and store the resulting PUF model corresponding to the device in the edge server node. Moreover, to meet the need for efficient and secure mutual authentication, we propose device authentication schemes for intra-domain authentication and cross-domain authentication, respectively. Finally, we discuss the key technologies involved in the proposed authentication framework and other application scenarios of PUF technology in distributed cloud systems.