Generative Topographic Mapping (GTM) is a non-linear latent variable model of the manifold learning family that provides simultaneous visualization and clustering of high-dimensional data. It was originally formulated as a constrained mixture of Gaussian distributions, for which the adaptive parameters were determined by Maximum Likelihood (ML), using the Expectation-Maximization (EM) algorithm. In this paper, we define an alternative variational formulation of GTM that provides a full Bayesian treatment to a Gaussian Process (GP) - based variation of the model.