Diffusion of gaseous solvents in bitumen is one of the imperative factors in studying solvent-aided thermal recovery processes. Experiments have shown significant swelling of bitumen upon diffusion of some gaseous solvents. Among different techniques for measurement of diffusion coefficient, Pressure Decay methods are the most popular. In one approach, liquid is placed in a cell overlaid by a gas cap. Diffusion of gas into the liquid at constant cell pressure can be achieved by continuously supplying the makeup gas into the gas cap. Different analytical and numerical models to estimate the molecular diffusion based on the mass of the injected gas have been proposed in the literature. However, there are two drawbacks associated with the previous models: 1) most of these models have been developed based on a no-swelling assumption while experiments have shown the significant swelling of bitumen upon diffusion of some solvents; 2) the models that incorporate the effect of swelling are numerical or semi-analytical and they are computationally-expensive, not straightforward, and prone to numerical error. Therefore, there is need for a simple analytical model that not only includes the swelling effect, but also is easy to implement. This study presents a novel analytical model obtained based on similarity solution along with a simple graphical method to estimate diffusion coefficients of gases in liquids. The experimental data of a moving interface as a result of swelling is used as an input to the developed model to estimate the diffusion coefficient. The developed model is applied to the available data in the literature and the predicted diffusion coefficients are compared to the previously reported ones. Moreover, the presented model is used to interpret new experimental data of nC(4)-nC(10) system to estimate the molecular diffusion coefficient. The developed model and the experimental data find applications in design and optimization of solvent-aided thermal recovery of bitumen and heavy oils.