High internal phase emulsions (HIPE) are immiscible liquid-liquid dispersions in which the physical packing limit of monodispersed spherical droplets can be surpassed through deformation of droplets to polyhedrons. By polymerizing the continuous phase of the HIPE and then extracting the dispersed phase, open-cell foams known as poly(HIPE) can be produced. The general morphology of poly(HIPE) foams consists of cavities (voids), originally occupied by the emulsion droplets, with holes between neighboring voids (windows) that connect the voids. The diffusion process in porous poly(HIPE) systems is modeled by the motion of a massless Brownian particle exhibiting a simple random walk. The mean escape time of the particle to leave a single void within the poly(HIPE) is a narrow escape problem. The complex void network of the poly(HIPE) is described as a series of connected repeating two-dimensional squares and the pathway of a single, massless particle is simulated in voids with different void to window dimension ratios. As a result, the dependence of mean escape time on the void to window ratio as well as void dimensions is determined, and an equation is developed to predict the mean escape time of a particle as a function of void size and ratio void/window. The larger scale diffusion in poly(HIPE) is modeled as a discrete random walk among a disordered network of voids that exhibit random size and window/void ratios. Diffusion is calculated by adding the mean escape time for each void in the particle walk.