Classical approaches to visualization directly reduce a document's high-dimensional representation into visualizable two or three dimensions, using techniques such as multidimensional scaling. More recent approaches consider an intermediate representation in topic space, between word space and visualization space, which preserves the semantics by topic modeling. We call the latter semantic visualization problem, as it seeks to jointly model topic and visualization. While previous approaches aim to preserve the global consistency, they do not consider the local consistency in terms of the intrinsic geometric structure of the document manifold. We therefore propose an unsupervised probabilistic model, called Semafore, which aims to preserve the manifold in the lower-dimensional spaces. Comprehensive experiments on several real-life text datasets of news articles and web pages show that Semafore significantly outperforms the state-of-the-art baselines on objective evaluation metrics.