Using Car-Parrinello molecular dynamics a structural diffusion mechanism for the simplest hydrophobic species in water, an H atom, is proposed. The hydrophobic solvation cavity is a highly dynamical aggregate that actually drives, by its own hydrogen-bond fluctuations, the diffusion of the enclosed solute. This makes possible an anomalously fast diffusion that falls only short of that of "Grotthuss structural diffusion" of H+ in water. Here, the picture of a static, i.e., "iceberglike," clathrate cage is a misleading concept. The uncovered scenario is similar to the "dynamical hole mechanism" found in a very different context, that is, large molecules moving in hot polymeric melts.