We present the Large PSG Model (LPSGM), a unified and flexible framework for sleep staging and disease diagnosis using polysomnography (PSG) data. LPSGM is designed to address the challenges of cross-center generalization in sleep staging and to enable fine-tuning for downstream disease diagnosis tasks. LPSGM introduces a unified training framework for heterogeneous datasets and allows flexible channel input adjustments during inference. The model is first trained on 220,500 hours whole-night PSG from 16 public datasets, achieving robust sleep staging performance. It is then fine-tuned on target center data for various disease classification tasks, including narcolepsy diagnosis, anxiety and depression detection, and the classification of healthy versus depressed individuals. LPSGM outperforms baseline models on both sleep staging and disease diagnosis tasks. Our results demonstrate that LPSGM not only enhances sleep staging accuracy but also improves the diagnosis of sleep-related and psychiatric disorders, showing promise for clinical applications in sleep medicine and psychiatry.