A complete picture of Fe self-diffusion in epitaxial L1(0)-ordered FePt thin films is presented. Isotopic multilayers of [(FePt)-Fe-57/(FePt)-Fe-nat](10) on MgO(110) were annealed at temperatures between 653 and 743 K. Nuclear resonant scattering reveals the decay of the isotopic superstructure due to diffusion. The well-defined orientation of the lattice in FePt-thin films allows us to resolve the strong anisotropy of diffusion in the tetragonal structure. The diffusion along the a-axes of the L1(0) structure is up to two orders of magnitude faster than along the c-axis, which is in line with the commonly assumed diffusion mechanism in this structure. The anisotropy is therefore much higher than in comparable structures such as TiAl. An important subtopic of the study is to compare the classical kinematical evaluation to an analysis employing the full dynamical scattering theory including hyperfine parameters of the nuclear resonances.