Title: A deep top-down approach to hierarchically coherent probabilistic forecasting . Abstract: Probabilistic, hierarchically coherent forecasting is a key problem in many practical forecasting applications -- the goal is to obtain coherent probabilistic predictions for a large number of  time series  arranged in a pre-specified tree hierarchy.  In this paper, we present a probabilistic top-down approach to hierarchical forecasting that uses a novel attention-based RNN model to learn the distribution of the proportions according to which each parent prediction is split among its children nodes at any point in time. These probabilistic proportions are then coupled with an independent univariate probabilistic forecasting model for the root time series. The resulting forecasts are naturally coherent, and provide probabilistic predictions over all time series in the hierarchy. We experiment on several public datasets and demonstrate significant improvements up to 27% on most datasets compared to state-of-the-art probabilistic hierarchical models. Finally, we also provide theoretical justification for the superiority of our top-down approach compared to traditional bottom-up modeling.