This paper investigates the application of deep neural networks to precipitation estimation from remotely sensed information. Specifically, a stacked denoising auto-encoder is used to automatically extract features from the infrared cloud images and estimate the amount of precipitation, referred as PERSIANN-SDAE. Due to the challenging imbalance in precipitation data, a Kullback-Leibler divergence is incorporated in the objective function to preserve the distribution of it. PERSIANN-SDAE is compared with a shallow neural network with hand designed features and an operational satellite-based precipitation estimation product. The experimental results demonstrate the effectiveness of PERSIANN-SDAE in estimating precipitation accurately while preserving its distribution. It outperforms both the shallow neural network and the operational product.