Continuous manufacturing of polymer films requires the efficient removal of solvent contents; drying performance is thus one of the major considerations in selecting the film formulation. The total drying time is often dominated by the final stage of drying where a small amount of moisture needs to diffuse across a film of mostly solid components. In this presentation we will first focus on the limit of extremely low solvent concentration. Diffusion of small molecules in amorphous polymers is known to follow a form of so-called hopping motion: penetrant molecules are trapped in microscopic cavities for extended time periods, and diffusion is made possible by rare but fast jumps between neighboring cavities. We study the molecular mechanism of these hopping motions by statistically analyzing the transition path ensembles associated with individual hopping events. Our investigation shows that a hopping event starts when the solvent molecule is able to (1) find a pathway between cavities that is prone to deformation and (2) break the hydrogen bonds it has formed with the polymer matrix in the original cavity. Our discussion will then extend to the regime of finitely-low solvent concentration where both the spatial distribution of solvent molecules and the swelling of the polymer matrix can affect the diffusion rate. The study offers atomistic insights into the drying of cast polymer films at the stage of the most practical significance, which will provide guidelines for polymer formulation design at the molecular level for enhanced drying properties.