We report molecular simulation studies of the diffusion processes in ice and CO2 clathrate hydrates performed using classical potential models of water (SPC/E) and carbon dioxide (EPM2). The diffusivity of H2O in ice is calculated to be 1.3x10(-18) m(2) s(-1) at 200 K using molecular dynamics simulations, a result in good agreement with experimental data. We also computed the diffusivity of H2O and CO2 in clathrate hydrates using both molecular dynamics and Monte Carlo simulations together with the Landau free energy method. We calculated free energy barriers for the CO2 hopping between clathrate cages with and without a water defect present. We determined that a water vacancy was necessary for diffusion of CO2, and we estimated the diffusion coefficient of CO2 molecules in clathrate hydrates to be 1x10(-12) m(2) s(-1) at 273 K and H2O in the clathrate hydrates to be 1x10(-23) m(2) s(-1) at 200 K.