Diffusion of atomic and molecular hydrogen in the interstitial space between graphite sheets has been studied by molecular dynamics simulations. Interatomic interactions were modeled by a tight-binding potential fitted to density-functional calculations. Atomic hydrogen is found to be bounded to C atoms, and its diffusion consists in jumping from a C atom to a neighboring one, with an activation energy of about 0.4 eV. Molecular hydrogen is less attached to the host sheets and diffuses faster than isolated H. At temperatures lower than 500 K, H 2 diffuses with an activation energy of 89 meV, whereas at higher T its diffusion is enhanced by longer jumps of the molecule as well as by correlations between successive hops, yielding an effective activation energy of 190 meV.