Diffusion models are models that describe the spread of anything -- atoms, ideas, people, seizures. They have developed independently across fields, from economics, computer science, and physics, to biology and medicine. They have a wide variety of applications including modeling the spread of pathogens, information, and ideas. In this dissertation, diffusion models are applied to modeling the spread of seizures. Our ability to predict how seizures spread -- its timing, speed, extent of activity, where seizures start and where seizures go -- can help us solve a critical problem in the effective treatment of refractory epilepsy: localization of seizure onset for its eventual resection, ablation, or neuromodulation. This dissertation encompasses a multidisciplinary approach (from analyses of signals and networks to newer methods in deep learning) across many brain states (from interictal, preictal, ictal to postictal) and with multimodal data (from structure to function, MRI to EEG) in different outcomes of epilepsy patients (from good to poor). New hypotheses about epilepsy pathophysiology are presented in the original research section of this dissertation, a new framework on the conceptualization of brain atlas is presented in Chapter 5, a taxonomy of seizure spread patterns is presented in Chapter 6, the investigation of white matter EEG recordings is presented in Chapter 7 -- this dissertation contains work more than about diffusion models applied to epilepsy; however the research and ideas presented throughout this work show promise for using diffusion models, or other models of epilepsy, to solve a clinical problem in epilepsy and hopefully improve our patients' quality of life.