Aerosol-cloud interactions constitute the largest source of uncertainty in assessments of the anthropogenic climate change. This uncertainty arises in part from the difficulty in measuring the vertical distributions of aerosols. We often have to settle for less informative vertically aggregated proxies such as aerosol optical depth (AOD). In this work, we develop a framework to infer vertical aerosol profiles using AOD and readily available vertically resolved meteorological predictors such as temperature or relative humidity. We devise a simple Gaussian process prior over aerosol vertical profiles and update it with AOD observations. We validate our approach using ECHAM-HAM aerosol-climate model data. Our results show that, while simple, our model is able to reconstruct realistic extinction profiles with well-calibrated uncertainty. In particular, the model demonstrates a faithful reconstruction of extinction patterns arising from aerosol water uptake in the boundary layer.