The diffusion coefficient of gaseous solvents in bitumen is an essential parameter in the design and evaluation of performance of solvent-assisted thermal recovery methods. Several analytical and numerical models have been developed as forward models for estimation of diffusion coefficient from experimental data based on various assumptions. However, many critical physical mechanisms such as swelling of the bitumen by solvent dissolution, the swelling-induced advective transport, and the mixture density change by solvent diffusion into the bitumen have not been considered in the previous studies. A simple analytical solution accounting for these mechanisms is lacking and the numerical solution with these mechanisms are computationally-intensive and prone to numerical dispersion. In this study, a novel analytical model is developed to determine the molecular diffusion coefficient of gaseous solvents into the bitumen, including all of the above-mentioned physical processes. The required experimental data for this analytical model are the swelling height (gas-liquid interface movement) with time, during the dissolution of a gaseous solvent at constant pressure in a liquid column. The diffusion coefficients predicted by the present model are compared with values reported in previous studies with different solvents and oil samples. The developed model is able to provide a simple and accurate estimation of the diffusion coefficient from the swelling data with the least number of assumptions. This study provides an improved methodology for estimating the diffusion coefficient of soluble gases in bitumen in systems that exhibit appreciable oil swelling and oil density change.