Our understanding of the wiring map of the brain, known as the connectome, has increased greatly in the last decade, mostly due to technological advancements in neuroimaging techniques and improvements in computational tools to interpret the vast amount of available data. Despite this, with the exception of the C. elegans roundworm, no definitive connectome has been established for any species. In order to obtain this, tracer studies are particularly appealing, as these have proven highly reliable. The downside of tract tracing is that it is costly to perform, and can only be applied ex vivo. In this paper, we suggest that instead of probing all possible connections, hitherto unknown connections may be predicted from the data that is already available. Our approach uses a ‘latent space model’ that embeds the connectivity in an abstract physical space. Regions that are close in the latent space have a high chance of being connected, while regions far apart are most likely disconnected in the connectome. After learning the latent embedding from the connections that we did observe, the latent space allows us to predict connections that have not been probed previously. We apply the methodology to two connectivity data sets of the macaque, where we demonstrate that the latent space model is successful in predicting unobserved connectivity, outperforming two baselines and an alternative model in nearly all cases. Furthermore, we show how the latent spatial embedding may be used to integrate multimodal observations (i.e. anterograde and retrograde tracers) for the mouse neocortex. Finally, our probabilistic approach enables us to make explicit which connections are easy to predict and which prove difficult, allowing for informed follow-up studies. Author summary: Tract tracing is a highly accurate procedure for identifying animal brain connectivity. However, the technique is labor intensive and requires the sacrifice of animal subjects. In our work, we describe a computational method that is able to predict the presence or absence of unobserved connections, without having to probe these connections physically. The model works by learning for each of the nodes in the connectome its position in a latent space. Nodes that are connected according to the available data are placed close to one another, while disconnected nodes are positioned far apart. Unobserved connections may now be inferred by looking at the corresponding distance in the latent space. We apply the procedure to two data sets of the macaque brain and show that the latent space model is able to predict the strength of unknown connections. Furthermore, we use the model to integrate anterograde and retrograde data for the mouse connectome. Because the model is probabilistic, it allows us to quantify how certain we are about our predictions. This enables future research to determine which connections can confidently predicted, and which connections require further data acquisition.