Light-induced isomerization processes in azobenzene-containing polymers produce mass transport that is of much interest for nanoscale imaging and lithography. Yet, despite the development of numerous models to simulate the mass transport mechanism, no model precisely describes all the experimental observations. We develop a new statistical approach that correctly reproduces light-driven mass motion in azobenzene-containing polymers with a high degree of accuracy. Comparisons with experiments show that our model predicts the nanoscale topographic modifications for many different incident field configurations, including optical near-fields produced by plasmonic structures with complex polarization states. In particular, the model allows the detailed molecular motions that lead to these topographic modifications to be identified.