  This is an expository article on the score-based diffusion models, with a
particular focus on the formulation via stochastic differential equations
(SDE). After a gentle introduction, we discuss the two pillars in the diffusion
modeling -- sampling and score matching, which encompass the SDE/ODE sampling,
score matching efficiency, the consistency models, and reinforcement learning.
Short proofs are given to illustrate the main idea of the stated results. The
article is primarily a technical introduction to the field, and practitioners
may also find some analysis useful in designing new models or algorithms.
