Force-directed layout algorithms are ubiquitously used tools for network visualization. However, existing algorithms either lack clear interpretation, or they are based on techniques of dimensionality reduction which simply seek to preserve network-immanent topological features, such as geodesic distance. We propose an alternative layout algorithm. The forces of the algorithm are derived from latent space models, which assume that the probability of nodes forming a tie depends on their distance in an unobserved latent space. As opposed to previous approaches, this grounds the algorithm in a plausible interaction mechanism. The forces infer positions which maximise the likelihood of the given network under the latent space model. We implement these forces for unweighted, multi-tie, and weighted networks. We then showcase the algorithm by applying it to Facebook friendship, and Twitter follower and retweet networks; we also explore the possibility of visualizing data traditionally not seen as network data, such as survey data. Comparison to existing layout algorithms reveals that node groups are placed in similar configurations, while said algorithms show a stronger intra-cluster separation of nodes, as well as a tendency to separate clusters more strongly in multi-tie networks, such as Twitter retweet networks.