Different layouts can characterize different aspects of the same graph. Finding a "good" layout of a graph is thus an important task for graph visualization. In practice, users often visualize a graph in multiple layouts by using different methods and varying parameter settings until they find a layout that best suits the purpose of the visualization. However, this trial-and-error process is often haphazard and time-consuming. To provide users with an intuitive way to navigate the layout design space, we present a technique to systematically visualize a graph in diverse layouts using deep generative models. We design an encoder-decoder architecture to learn a model from a collection of example layouts, where the encoder represents training examples in a latent space and the decoder produces layouts from the latent space. In particular, we train the model to construct a two-dimensional latent space for users to easily explore and generate various layouts. We demonstrate our approach through quantitative and qualitative evaluations of the generated layouts. The results of our evaluations show that our model is capable of learning and generalizing abstract concepts of graph layouts, not just memorizing the training examples. In summary, this paper presents a fundamentally new approach to graph visualization where a machine learning model learns to visualize a graph from examples without manually-defined heuristics.