Molecular dynamics (MD) simulations were employed to estimate the diffusion coefficients of small gas molecules (Ar, O2, N2, CO2, and CH4) in amorphous cis-1,4-polybutadiene in the temperature range of 250-400 K. The VT diagram and solubility parameter of the amorphous polymer have been successfully reproduced using a full atomistic potential. Diffusion coefficients were calculated from long NPT MD runs (up to 3 ns) at temperature ranging from 250 up to 400 K. Calculated diffusion coefficients compare well with experimental data as well as previous published work, though a systematic overestimation is found due to the finite-size effect of the model. The influence of various physical and computational parameters on the results is discussed. The diffusion mechanism is examined at the different temperatures of study.