The rapid expansion of Location-Based Social Networks (LBSNs) has highlighted the importance of effective next Point-of-Interest (POI) recommendations, which leverage historical check-in data to predict users' next POIs to visit. Traditional centralized deep neural networks (DNNs) offer impressive POI recommendation performance but face challenges due to privacy concerns and limited timeliness. In response, on-device POI recommendations have been introduced, utilizing federated learning (FL) and decentralized approaches to ensure privacy and recommendation timeliness. However, these methods often suffer from computational strain on devices and struggle to adapt to new users and regions. This paper introduces a novel collaborative learning framework, Diffusion-Based Cloud-Edge-Device Collaborative Learning for Next POI Recommendations (DCPR), leveraging the diffusion model known for its success across various domains. DCPR operates with a cloud-edge-device architecture to offer region-specific and highly personalized POI recommendations while reducing on-device computational burdens. DCPR minimizes on-device computational demands through a unique blend of global and local learning processes. Our evaluation with two real-world datasets demonstrates DCPR's superior performance in recommendation accuracy, efficiency, and adaptability to new users and regions, marking a significant step forward in on-device POI recommendation technology.