Modern clinical and animal scanners offer versatile options for diffusion MRI, including very high b-values, at which the conventional perturbative description and related model are not applicable. We demonstrate this failure for any nontrivial domain with a boundary, regardless its shape and permeability. Since the magnetization is localized near boundaries, the signal becomes more sensitive to the microstructure. Even the signal from the extracellular diffusion is shown to be non-Gaussian at high b-values. These non-Gaussian features offer new imaging modalities at ordinary gradients accessible on most MRI scanners but, if unnoticed, they may result in misleading biomedical interpretations.