Diffusion of gas across liquid films between bubbles is thought to increase average bubble size in foam in porous media. It is cited as one reason why foams for enhanced oil recovery (EOR) are less resistant to flow than foams and why mixing with steam increases the resistance of steam foam. In porous media, diffusion can rapidly destroy bubbles smaller than a pore, but in EOR foam bubbles are thought to be larger than pores. This study examines the effect of inter-bubble gas diffusion on flowing bubbles in a periodically constricted tube and, in particular, its effect on the bubble-size distribution and capillary resistance to flow. The study is based on the solution for bubble shapes, curvatures, and pressure differences between bubbles from previous studies of bubble movement through periodically constricted tubes. It uses these results to estimate the diffusion rate between bubbles. 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, because 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. Instead it modestly increases the resistance to flow. The reason for the apparent weakness of foam therefore evidently lies in factors other than 's large diffusion rate through foam.