In this work, we perform a study of the off-center effect on the diffusion coefficient and we propose a new mechanism for fast diffusion. The model assumes that the equilibrium positions of the cationic impurities are noncentral and that the diffusion proceeds by hopping across the potential barrier along the nonlinear paths with the highest probability [1]. The nonlinear paths between two consecutive positions characterize even the self-diffusion and furthermore, in the off-center diffusion this path is appropriate. The main results is that the off-center position considerably enhances the diffusion. The theoretical diffusion coefficients have been obtained by modeling the potential barrier. Changes of the configuration entropy and the vibration spectra due to the presence of the noncentral impurity are included in the model. We emphasize the good agreement of the model with the experimental data for KCl:Cu+and show that if the impurity is placed close to the central site, the appropriate diffusion coefficient is close to that for the cationic self-diffusion. We proceeded in the Li+cation case as in the case of Cu+cation.