Trajectory modeling is a long-standing challenge in the application of computational methods to health care. In the age of big data, traditional statistical and machine learning methods do not achieve satisfactory results as they often fail to capture the complex underlying distributions of multimodal health data and long-term dependencies throughout medical histories. Recent advances in generative artificial intelligence (AI) have provided powerful tools to represent complex distributions and patterns with minimal underlying assumptions, with major impact in fields such as finance and environmental sciences, prompting researchers to apply these methods for disease modeling in health care. While AI methods have proven powerful, their application in clinical practice remains limited due to their highly complex nature. The proliferation of AI algorithms also poses a significant challenge for nondevelopers to track and incorporate these advances into clinical research and application. In this paper, we introduce basic concepts in generative AI and discuss current algorithms and how they can be applied to health care for practitioners with little background in computer science. We surveyed peer-reviewed papers on generative AI models with specific applications to time-series health data. Our search included single- and multimodal generative AI models that operated over structured and unstructured data, physiological waveforms, medical imaging, and multi-omics data. We introduce current generative AI methods, review their applications, and discuss their limitations and future directions in each data modality. We followed the PRISMA-ScR (Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for Scoping Reviews) guidelines and reviewed 155 articles on generative AI applications to time-series health care data across modalities. Furthermore, we offer a systematic framework for clinicians to easily identify suitable AI methods for their data and task at hand. We reviewed and critiqued existing applications of generative AI to time-series health data with the aim of bridging the gap between computational methods and clinical application. We also identified the shortcomings of existing approaches and highlighted recent advances in generative AI that represent promising directions for health care modeling.