Diffusivities of methyl acetate, methanol and water in poly(vinyl acetate) and fully and partially hydrolyzed poly(vinyl alcohol) have been measured by capillary column inverse gas chromatography and/or gravimetric sorption. Data from the literature have been used when available for comparison. Overall the diffusivities show good consistency in terms of their temperature and concentration dependences. The free‐volume model has been applied to all the data with excellent results. In most cases the dramatic changes in diffusivities with temperature and concentration can be captured using only a few experimental data points and two regression parameters. This demonstrates that the free‐volume theory is a valuable tool for the design of equipment for processing and devolatilization of polymer − solvent systems. © 2013 Society of Chemical Industry