This chapter presents stochastic models of molecular diffusion together with some important properties of the diffusion process. Diffusion models based on both position-jump processes and velocity-jump processes are analysed. The position-jump processes include the SDE-based approach (introduced in Chapter 3) together with the compartment-based (lattice-based) modelling, described by the diffusion master equation. Boundary conditions for the diffusion process are then discussed, including systems in which molecules are adsorbed by surfaces and models with a chemically reactive boundary. The Einstein–Smoluchowski relation between the diffusion constant and the size of the molecule is derived.