Knudsen diffusion is approximately valid when the channel diameters are much larger than molecular diameters, adsorption forces are weak or negligible, and the only obstacles are molecule-wall collisions. The ray lengths between walls are distributed over an enormous range, and there is no upper bound for occasional extreme outliers. A Monte Carlo simulation produces an enormous range in the distribution of diffusivities, which follows a log-normal distribution. A reasonably accurate estimation of diffusivity requires more than 10,000 runs. The principal types of one-dimensional channels are the zig-zag channels and the connected cavities, and they have diffusivities that are much lower than the straight channels. The principal cause is lower vista which reduces the extreme lengths of the outlier rays, and the contributing causes are tortuosity, and negative correlation which increases the probability that consecutive steps are in opposite directions. The principal types of two-dimensional channels investigated are: rectangular, oblique, brick, hexagon, and straight-sinusoid or MEI type. They give rise to highly anisotropic diffusion tensors. (c) 2014 Elsevier Ltd. All rights reserved.