A series of vapor-deposited poly(amic acid) (PAA) films were exposed to dimethyl sulfoxide (DMSO) vapors to investigate sorption kinetics and surface smoothing phenomena. Gravimetric sorption and secondary-ion mass spectrometry (SIMS) results are both consistent with frontal (case II) diffusion. These experiments suggest that the solvent front is defined by a sharp interface that delineates the swollen material from the unswollen material. Solvent-vapor smoothing was studied by first depositing PAA onto rough aluminum surfaces, and then, during solvent-vapor exposure, the surface topology was continuously monitored using a light interference microscope. The resulting time-dependent power spectra indicate that high-frequency defects smooth faster than low-frequency defects. This frequency dependence was further investigated by depositing PAA onto a series of sinusoidal surfaces and exposing them to solvent vapor inside a flow channel. The sinusoidal amplitudes decay exponentially with time, with decay constants that are proportional to the surface frequency. To explain the physics of surface smoothing, a two-parameter model is presented and agrees qualitatively with experimental data.