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.