  We study the real-time and real-space dynamics of charge in the
one-dimensional Hubbard model in the limit of high temperatures. To this end,
we prepare pure initial states with sharply peaked density profiles and
calculate the time evolution of these nonequilibrium states, by using numerical
forward-propagation approaches to chains as long as 20 sites. For a class of
typical states, we find excellent agreement with linear-response theory and
unveil the existence of remarkably clean charge diffusion in the regime of
strong particle-particle interactions. Moreover, we demonstrate that this
diffusive behavior does not depend on certain details of our initial
conditions, i.e., it occurs for five different realizations with random and
nonrandom internal degrees of freedom, single and double occupation of the
central site, and displacement of spin-up and spin-down particles.
