We propose a novel self-diffusion model for ionic liquids on an atomic level of detail. The model is derived from molecular dynamics simulations of guanidinium-based ionic liquids (GILs) as a model case. The simulations are based on an empirical molecular mechanical force field, which has been developed in our preceding work, and it relies on the charge distribution in the actual liquid. The simulated GILs consist of acyclic and cyclic cations that were paired with nitrate and perchlorate anions. Self-diffusion coefficients are calculated at different temperatures from which diffusive activation energies between 32-40 kJ/mol are derived. Vaporization enthalpies between 174-212 kJ/mol are calculated, and their strong connection with diffusive activation energies is demonstrated. An observed formation of cavities in GILs of up to 6.5% of the total volume does not facilitate self-diffusion. Instead, the diffusion of ions is found to be determined primarily by interactions with their immediate environment via electrostatic attraction between cation hydrogen and anion oxygen atoms. The calculated average time between single diffusive transitions varies between 58-107 ps and determines the speed of diffusion, in contrast to diffusive displacement distances, which were found to be similar in all simulated GILs. All simulations indicate that ions diffuse by using a brachiation type of movement: a diffusive transition is initiated by cleaving close contacts to a coordinated counterion, after which the ion diffuses only about 2 A until new close contacts are formed with another counterion in its vicinity. The proposed diffusion model links all calculated energetic and dynamic properties of GILs consistently and explains their molecular origin. The validity of the model is confirmed by providing an explanation for the variation of measured ratios of self-diffusion coefficients of cations and paired anions over a wide range of values, encompassing various ionic liquid classes as well as the simulated GILs. The proposed diffusion model facilitates the qualitative a priori prediction of the impact of ion modifications on the diffusive characteristics of new ionic liquids.