The effects of the polydispersity of the characteristic diffusion length of the pore space of fibrous media on the effective diffusion coefficients of gases are studied by investigating the problem of gaseous diffusion in the Knudsen, transition, and bulk regimes in square arrays of filament bundles, of cylindrical cross section consisting of unidirectional, freely overlapping cylindrical filaments. Effective diffusion coefficients are computed using a stochastic simulation method based on the computation of the mean square displacement of a large number of molecules (random walkers) diffusing in the pore space. The dependence of effective diffusivity on filament to bundle radius ratio, intrabundle porosity, interbundle porosity, and Knudsen number is investigated in detail. The computed diffusivities are compared to the predictions of analytical or semianalytical formulas based on expressions derived in the literature for two-phase media or bidisperse pore structures.