  We consider the general problem of the first passage distribution of
particles whose displacements are subject to time delays. We show that this
problem gives rise to a \emph{propagation-dispersion equation} which is
obtained as the continuous limit of the exact microscopic \emph{first visit
equation}. The propagation-dispersion equation should be contrasted with the
advection-diffusion equation as the roles of space and time are reversed, hence
the name \emph{temporal diffusion}, which is a generic behavior encountered in
an important class of systems.
