A large fraction of the rain received by continental India is produced by cyclonic vortices with outer radii of about 1000 km that are contained within the larger scale South Asian monsoon flow. The more intense occurrences of these vortices are called monsoon depressions; these consist of bottom-heavy columns of relative vorticity that propagate to the northwest in time-mean low-level eastward flow. Previous studies have argued that this apparent upstream propagation is caused by dynamical lifting west of the vortex centre, with the resulting ascent producing vortex stretching that shifts the vortex to the west. Here, analysis of over 100 Indian monsoon depressions is used to show that low-level vortex stretching has a spatial structure inconsistent with the observed propagation and is balanced by other terms in the low-level vorticity budget. Instead, monsoon depressions are shown to consist of potential vorticity maxima that have peak amplitude in the middle troposphere and propagate westward by nonlinear, horizontal adiabatic advection (i.e. beta drift). The precipitating ascent in monsoon depressions makes a more minor contribution to the total storm motion and primarily acts to maintain the upright structure of the vortex. These results suggest a new view of Indian monsoon depressions as potential vorticity columns that propagate primarily by adiabatic dynamics.