The Principles of Diffusion Models: Real-Time Continuous & Discrete Diffusion

In recent years, diffusion models have become a central paradigm in computer vision, powering advances in image synthesis, editing, and video generation. However, existing tutorials are often fragmented, focusing either on specific applications or isolated methodological perspectives without a unifying framework. This tutorial aims to present a principle-driven view of diffusion models by distilling their foundations into a small set of core ideas that unify variational, score-based, and flow-based approaches. It further emphasizes emerging directions in real-time generation through flow-map models, which enable fast and interactive visual applications. In addition, the tutorial extends this framework to discrete and tokenized diffusion models, highlighting their role in bridging continuous vision generation with multimodal and structured representations.