Score-based Diffusion Models via Stochastic Differential Equations – a Technical Tutorial

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 model, and reinforcement learning. Short proofs are given to illustrate the main idea of the stated results. The article is primarily for introducing the beginners to the field, and practitioners may also find some analysis useful in designing new models or algorithms.