We predict the conditional distributions of service metrics, such as response time or frame rate, from infrastructure measurements in a cloud environment. From such distributions, key statistics of the service metrics, including mean, variance, or percentiles can be computed, which are essential for predicting SLA conformance or enabling service assurance. We model the distributions as Gaussian mixtures, whose parameters we predict using mixture density networks, a class of neural networks. We apply the method to a VoD service and a KV store running on our lab testbed. The results validate the effectiveness of the method when applied to operational data. In the case of predicting the mean of the frame rate or response time, the accuracy matches that of random forest, a baseline model.