Diffusion and flow through cigarette paper are both important transport mechanisms to achieve desired smoke yields, especially with respect to carbon monoxide, or to pass legislative requirements, such as reduced ignition propensity. The pore size distribution of cigarette paper, as it can be measured, for example, by mercury porosimetry has been shown to be a useful tool for the prediction of diffusion constants and of air permeability. This tool, however, suffers from an important drawback. The pore size distribution, as delivered by mercury porosimetry, is the pore volume as a function of the pore radius and does not contain information on the number of pores or on the length of the pores. But this information is needed to calculate the diffusion constant and the air permeability. In the present study this problem is solved by stochastic simulation of the pore shape based on a discrete random-walk model. The paper is discretised into small cells and uniform probabilities for the transition from one cell to the other are chosen. The generated random-walk is considered a pore, if it passes from one side of the paper to the other side without intersecting itself. A large number of such pores is simulated and their length distribution for a given radius is determined from the simulation results. From these results the number of pores can be estimated and the diffusion constant and the air permeability can be calculated. A comparison of calculated results and measured diffusion constants and air permeabilities of 18 naturally porous cigarette papers shows a very good agreement with an R² greater than 0.95. Furthermore it is possible to explain from measurements and calculations how the paper composition affects the pore size distribution and consequently the diffusion constant and the air permeability.