In this paper, we numerically study the influence of pore structures on diffusion processes in porous media. The porous media geometry models are constructed based on two-dimensional Voronoi diagrams, and they feature randomly connected channels with large pores embedded to simulate the heterogeneity of porous media. A link-type two-relaxation-time (LTRT) lattice Boltzmann (LB) method is employed to solve the diffusion equation. The tortuosity is characterized as a function of porosity and pore structure. From numerical results, a correlation for the tortuosity as a function of porosity is derived for Voronoi geometries without large pores. Geometries with large pores at the same total porosity have higher tortuosity, which indicates that geometric heterogeneity slows down the diffusion. (C) 2013 Elsevier Ltd. All rights reserved.