Inferring the true demand for a product or a service from aggregate data is often challenging due to the limited available supply, thus resulting in observations that are censored and correspond to the realized demand, thereby not accounting for the unsatisfied demand. Censored regression models are able to account for the effect of censoring due to the limited supply, but they don't consider the effect of substitutions, which may cause the demand for similar alternative products or services to increase. This paper proposes Diffusion-aware Censored Demand Models, which combine a Tobit likelihood with a graph diffusion process in order to model the latent process of transfer of unsatisfied demand between similar products or services. We instantiate this new class of models under the framework of GPs and, based on both simulated and real-world data for modeling sales, bike-sharing demand, and EV charging demand, demonstrate its ability to better recover the true demand and produce more accurate out-of-sample predictions.