Single-cell RNA sequencing (scRNA-seq) is a powerful technique that enables researchers to measure gene expression at the resolution of single cells. Because of the low amount of RNA present in a single cell, many genes fail to be detected even though they are expressed; these genes are usually referred to as dropouts. Here, we present a general and flexible zero-inflated negative binomial model (ZINB-WaVE), which leads to low-dimensional representations of the data that account for zero inflation (dropouts), over-dispersion, and the count nature of the data. We demonstrate, with simulations and real data, that the model and its associated estimation procedure are able to give a more stable and accurate low-dimensional representation of the data than principal component analysis (PCA). Furthermore, the model can be used to compute cell-specific weights to unlock bulk RNA-seq DE pipelines for zero-inflated data.