This article provides a technical tutorial on score-based diffusion models, focusing on their formulation via stochastic differential equations (SDEs). It introduces the two key pillars of diffusion modeling: sampling and score matching. The paper discusses the forward and backward processes of diffusion models, emphasizing the backward process as the core challenge, which requires time reversal of diffusion processes and score matching to learn the process. The article also covers the convergence of stochastic samplers, analyzing them in terms of total variation and Wasserstein-2 distances. It provides examples of various diffusion models, including the Ornstein-Uhlenbeck (OU) process, variance exploding (VE) SDE, variance preserving (VP) SDE, and contractive diffusion probabilistic models (CDPM). The paper also reviews score matching techniques, including implicit and sliced score matching, and denoising score matching, which are essential for learning the score function in diffusion models. Theoretical results are presented, along with practical considerations for implementing these models. The article serves as a comprehensive introduction to the field, offering insights into the design and analysis of diffusion models.This article provides a technical tutorial on score-based diffusion models, focusing on their formulation via stochastic differential equations (SDEs). It introduces the two key pillars of diffusion modeling: sampling and score matching. The paper discusses the forward and backward processes of diffusion models, emphasizing the backward process as the core challenge, which requires time reversal of diffusion processes and score matching to learn the process. The article also covers the convergence of stochastic samplers, analyzing them in terms of total variation and Wasserstein-2 distances. It provides examples of various diffusion models, including the Ornstein-Uhlenbeck (OU) process, variance exploding (VE) SDE, variance preserving (VP) SDE, and contractive diffusion probabilistic models (CDPM). The paper also reviews score matching techniques, including implicit and sliced score matching, and denoising score matching, which are essential for learning the score function in diffusion models. Theoretical results are presented, along with practical considerations for implementing these models. The article serves as a comprehensive introduction to the field, offering insights into the design and analysis of diffusion models.