The CO₂ transport process was studied in a series of amine-modified epoxy resins having different cross-linking densities but the same chemical environment for the penetrant molecules. Positron Annihilation Lifetime Spectroscopy (PALS) was used to monitor the free volume structure of the samples and experimentally evaluate their fractional free volume f_h(T) and its temperature evolution. The analysis of the free volume hole size distribution showed that all the holes have a size large enough to accommodate the penetrant molecules at temperatures T above the glass transition temperature T_g. The measured gas diffusion constants at T > T_g have been reproduced in the framework of the free volume theory of diffusion using a novel procedure based on the use of f_h(T) as an input experimental parameter.