Abstract The processes of diffusion in multi‐compartmental tissue models are discussed using an analytical model of diffusion with exchange. Diffusion in the intracellular compartment has been found to be highly restricted, with the apparent diffusion coefficient (ADC 1 ) dependent on the experimental parameters. Extracellular diffusion mediated by tortuosity, depends on tissue geometry, but not on the experimental conditions. Both the intra‐ and extracellular diffusion can be anisotropic and exhibit non‐monoexponential behavior. The cell membrane permeability is shown to significantly influence the diffusion measurement in tissues. In consequence, the phenomenological, bi‐exponential models of diffusion cannot directly estimate the intrinsic characteristics of intra‐ and extracellular water. The mechanisms of the ADC decrease after stroke are also discussed.