The diffusion of hydrogen through granular materials partly saturated with water was measured by a non-steady state technique previously described. The two types of sample used consisted of solid particles (unimodal poresize distribution) and porous particles (bimodal pore-size distribution), and all measurements were made on samples being dried from saturation. Coefficients of diffusion D were calculated, and for the range over which the larger pores were emptying the empirical equation D = D_v(/_v)^σ fitted all materials, where epsilon is the fractional air-filled volume, _v is the volume occupied by the larger-pore phase, and where D_v is the diffusion coefficient when only this phase is air-filled. For all materials σ approximately equals 4 whether the samples were uniform or of mixed sizes. No such relationship existed over the subsequent range in which the smaller pores were drained. Over this range D must be a function of at least five independent variables - the total porosity _T, the crumb porosity _c, the shape factor for the crumbs or inter-crumb pores k, the shape factor for the particles forming the crumbs or crumb pores k_c, and the moisture content of the sample. The spatial distribution of pores within a porous medium can be as important as the sizes of the pores. The factors k and m, previously introduced as particle-shape factors, now have a greater significance as measures of the geometrical complexity of a porous system. Adding water can either increase or decrease the complexity, depending on the amount added and the nature of the system. The agricultural significance of diffusion between the crumbs D_v and within the crumbs D_c is discussed, and it is suggested that D_c, or its associated complexity factor k_c, might be used as an index of soil structure.