The problem of bulk, transition and Knudsen regime diffusion in structures of freely overlapping fibers of various orientation distributions was numerically investigated, and the interrelation of the resulting effective diffusivities was examined. Fibers were randomly positioned and oriented in d = 1, 2, or 3 directions. A Monte Carlo simulation scheme was employed to determine the effective diffusivities from the mean-square displacement of random walkers traveling in the interior of the porous structure. The effective diffusivity was found to depend strongly on the orientational distribution of the fibers, porosity of the fibrous structures, and Knudsen number. The tortuosity factor decreased in general with increasing porosity, approaching at the limit of dilute beds the lower bound derived for each direction of diffusion from variational principles. The simulation results agreed well with experimental values of the bulk tortuosity of fibrous beds from the literature. It was also found that the reciprocal additivity or harmonic average effective diffusivity expression (Bosanquet formula), commonly used to estimate transition regime diffusivities from the values at the ordinary and Knudsen diffusion limits, provides an excellent approximation for the effective diffusivity of fibrous beds, except for that parallel to the fibers of a unidirectional structure.