The title of this book brings together the seemingly incompatible concepts. Indeed, it was always assumed that the dynamic regularities correspond to only fully orderly movement, rather than diffusive motion of the atoms. But this book shows that the interaction between the hydrogen atoms in the metal increases the degree of order in the system. This interaction manifests itself through the dependence of the diffusion coefficient on the concentration. This leads to many remarkable consequences. Diffusion theory of origin and evolution of the hydrogen concentration inhomogeneities is presented. The kinetic equation for the hydrogen in the hydride-forming metals is obtained, which generalizes the Cahn's theory of spinodal decomposition and its modifications on the general case of arbitrary concentration gradients. Solutions of this nonlinear equation describe the spatial and temporal structures of hydrogen. Equations of the collective dynamics of the hydrogen and metal sub-systems are obtained, and some of their solutions are presented. The book may be of interest not only for researchers, but also for undergraduate students of mathematical, physical, and metal science specialties.