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The diffusive tortuosity factor of a porous media quantifies the material’s resistance to diffusion, an important component of modeling flows in porous structures at the macroscale. Advances in X-ray micro-computed tomography (-CT) imaging provide the geometry of the material at the microscale (microstructure) thus enabling direct numerical simulation (DNS) of transport at the microscale. The data from these DNS are then used to close material’s macroscale transport models, which rely on effective material properties. In this work, we present numerical methods suitable for large scale simulations of diffusive transport through complex microstructures for the full range of Knudsen regimes. These numerical methods include a finite-volume method for continuum conditions, a random walk method for all regimes from continuum to rarefied, and the direct simulation Monte Carlo method. We show that for particle methods, the surface representation significantly affects the accuracy of the simulation for high Knudsen numbers, but not for continuum conditions. We discuss the upscaling of pore-resolved simulations to single species and multi-species volume-averaged models. Finally, diffusive tortuosities of a fibrous material are computed by applying the discussed numerical methods to 3D images of the actual microstructure obtained from X-ray computed micro-tomography.