The effective diffusivity of gaseous species in partially-saturated finite-size porous media is a valuable parameter for mathematical modeling of many processes, but it is difficult to measure experimentally. In this work, the effective diffusivity of carbon-fiber gas diffusion layers (GDLs) used in polymer electrolyte fuel cells (PEFCs) was determined by performing lattice Boltzmann (LB) simulations on X-ray tomographic reconstructions of invading water configurations. Calculations on dry GDLs were in close agreement with previous experimental data; the effective diffusivity was reduced by the addition of PTFE due to the loss of pore volume and the higher tortuosity of transport paths. The effect of water saturation was significantly larger. It was found that the resistance of water to gas transport was extremely dependent on the saturation distribution through the porous medium, particularly the peak saturation, and not just the average saturation as is typically considered in the literature. Through-plane diffusion was dramatically limited in materials with high-peak local saturations, even at low average saturation levels. No significant limitations were observed for diffusion in the material plane. The computed results demonstrate the strong sensitivity of finite-size porous media to local conditions, highlighting the difficulties of applying volume-averaged continuum-scale modeling techniques to micro-scale materials.