Accurate prediction of precipitation intensity is of crucial importance for both human and natural systems, especially in a warming climate more prone to extreme precipitation. Yet climate models fail to accurately predict precipitation intensity, particularly extremes. One missing piece of information in traditional climate model parameterizations is sub-grid scale cloud structure and organization, which affects precipitation intensity and stochasticity at the grid scale. Here we show, using storm-resolving climate simulations and machine learning, that by implicitly learning sub-grid organization, we can accurately predict precipitation variability and stochasticity with a low dimensional set of variables. Using a neural network to parameterize coarse-grained precipitation, we find mean precipitation is predictable from large scale quantities only; however, the neural network cannot predict the variability of precipitation (R 2 ∼ 0.4) and underestimates precipitation extremes. Performance is significantly improved when the network is informed by our novel organization metric, correctly predicting precipitation extremes and spatial variability (R 2 ∼ 0.95). The organization metric is implicitly learned by training the algorithm on high-resolution precipitable water, encoding organization degree and humidity amount at the subgrid-scale. The organization metric shows large hysteresis, emphasizing the role of memory created by sub-grid scale structures. We demonstrate this organization metric can be predicted as a simple memory process from information available at the previous time steps. These findings stress the role of organization and memory in accurate prediction of precipitation intensity and extremes and the necessity of parameterizing sub-grid scale convective organization in climate models to better project future changes in the water cycle and extremes.