How differential equations power modern image generation

Diffusion models generate images by slowly adding noise, then learning to reverse the process. This tutorial frames that intuition precisely: the forward process is governed by differential equations (both stochastic and deterministic), the reverse process follows from score matching, and existing methods like DDPM and DDIM emerge naturally as discrete approximations of the same underlying equations. The unification clarifies why different sampling strategies work and provides a foundation for understanding and extending diffusion-based generative models.