Deep learning is revolutionizing biological and medical research in recent years. However, due to the intrinsic stochastic property of biological processes, it is often difficult to build reliable predictive machine learning models, which map underlying genetic and environmental conditions to phenotypic observations. Specifically, even genetically identical cells in identical environments display variable phenotypes. This imposes a big challenge in building traditional supervised models which can only predict a determined phenotype (or a set of determined phenotypes) per genetic and environmental condition. Furthermore, the intrinsic noise has been proved to play a crucial role in gene regulation mechanisms. Predicting only the average value of the outputs is not sufficient in studying the dynamics of biological systems. We developed a deep learning algorithm that can predict the probability distribution of the phenotypes based on only one noisy observation for each input condition, without the prior knowledge or assumption of the probability distributions. This study can facilitate the quantitative understanding of biological systems as well as the design of synthetic gene circuits. *This study is supported by the National Science Foundation under Grant No. DBI-1548297.