Personalized diagnosis prediction based on electronic health records (EHR) of patients is a promising yet challenging task for AI in healthcare. Existing studies typically ignore the heterogeneity of diseases across different patients. For example, diabetes can have different complications across different patients (e.g., hyperlipidemia and circulatory disorder), which requires personalized diagnoses and treatments. Specifically, existing models fail to consider 1) varying severity of the same diseases for different patients, 2) complex interactions among syndromic diseases, and 3) dynamic progression of chronic diseases. In this work, we propose to perform personalized diagnosis prediction based on EHR data via capturing disease severity, interaction, and progression. In particular, we enable personalized disease representations via severity-driven embeddings at the disease level. Then, at the visit level, we propose to capture higher-order interactions among diseases that can collectively affect patients' health status via hypergraph-based aggregation; at the patient level, we devise a personalized generative model based on neural ordinary differential equations to capture the continuous-time disease progressions underlying discrete and incomplete visits. Extensive experiments on two real-world EHR datasets show significant performance gains brought by our approach, yielding average improvements of 10.70% for diagnosis prediction over state-of-the-art competitors.