While variational autoencoders have been successful in several tasks, the use\nof conventional priors are limited in their ability to encode the underlying\nstructure of input data. We introduce an Encoded Prior Sliced Wasserstein\nAutoEncoder wherein an additional prior-encoder network learns an embedding of\nthe data manifold which preserves topological and geometric properties of the\ndata, thus improving the structure of latent space. The autoencoder and\nprior-encoder networks are iteratively trained using the Sliced Wasserstein\ndistance. The effectiveness of the learned manifold encoding is explored by\ntraversing latent space through interpolations along geodesics which generate\nsamples that lie on the data manifold and hence are more realistic compared to\nEuclidean interpolation. To this end, we introduce a graph-based algorithm for\nexploring the data manifold and interpolating along network-geodesics in latent\nspace by maximizing the density of samples along the path while minimizing\ntotal energy. We use the 3D-spiral data to show that the prior encodes the\ngeometry underlying the data unlike conventional autoencoders, and to\ndemonstrate the exploration of the embedded data manifold through the network\nalgorithm. We apply our framework to benchmarked image datasets to demonstrate\nthe advantages of learning data representations in outlier generation, latent\nstructure, and geodesic interpolation.\n