Transport of gas across liquid films between bubbles is thought to weaken foam by increasing bubble size. It is cited as one reason why CO2 foams for enhanced oil recovery (EOR) are usually weaker than N2 foams and why steam foams are weaker than foams of steam mixed with N 2. In porous media, diffusion can rapidly destroy bubbles smaller than a pore, but in EOR foam bubbles are thought to be larger than pores, making the role of diffusion moot. Previous analysis of diffusion in foam in porous media has focused on diffusion between immobile bubbles smaller than the pores. We examine here the effect of inter-bubble gas diffusion on flowing bubbles in a simplified model of a porous medium (a periodically constricted tube) and in particular its effect on the bubble-size distribution and capillary resistance to flow. We use the solution for bubble shapes, curvatures and pressure differences between bubbles from previous studies of bubble movement through periodically constricted tubes to estimate the diffusion rate between bubbles. We fit our model parameters to mass-transfer data for foam films between bubbles and realistic convection rates and pore geometries for foam EOR processes. Bubbles somewhat smaller than a pore can indeed disappear by diffusion as the bubbles move. For bubbles larger than a pore, as expected in EOR, diffusion does not affect bubble size. Instead, diffusion actually increases capillary resistance to flow (i.e., makes foam stronger): lamellae spend more time in positions where lamella curvature resists forward movement. When fit to pressures and diffusion and convection rates representative of field application of foams, diffusion is not expected to alter the bubble-size distribution in a foam, but instead modestly increases the resistance to flow. The reason for the apparent weakness of CO2 foam therefore evidently lies in factors other than CO2's large diffusion rate through foam.