We use classical molecular dynamics and the modified embedded atom method formalism to investigate the dynamics of atomic-scale transport on a low-index model compound surface, TiN(001). Our simulations, totaling 0.25 μs for each case study, follow the pathways and migration kinetics of Ti and N adatoms, as well as TiN x complexes with x = 1-3, which are known to contribute to the growth of TiN thin films by reactive deposition from Ti, N 2 , and N precursors. The simulations are carried out at 1000 K, within the optimal range for TiN(001) epitaxial growth. We find Ti adatoms to be the highest-mobility species on TiN(001), with the primary migration path involving jumps of one nearest-neighbor distance d NN between adjacent fourfold hollow sites along in-plane 100 channels. Long jumps, 2d NN , are also observed, but at much lower frequency. N adatoms, which exhibit significantly lower migration rates than Ti, diffuse along in-plane 110 directions and, when they intersect other N atoms, associatively form N 2 molecules, which desorb at kinetic rates. As expected, TiN and TiN 3 complexes migrate at even lower rates with complex diffusion pathways involving rotations, translations, and rototranslations. TiN 2 trimers, however, are shown to have surprisingly high diffusion rates, above that of N adatoms and almost half that of Ti adatoms. TiN 3 motion is dominated by in-place rotation with negligible diffusion.