We introduce dynamic correlated topic models (DCTM) for analyzing discrete data over time. This model is inspired by the hierarchical Gaussian process latent variable models (GP-LVM). DCTM is essentially a non-linear dimension reduction technique which is capable of (1) detecting topic evolution within a document corpus, (2) discovering topic correlations between document corpora, (3) monitoring topic and correlation trends dynamically. Unlike generative aspect models such like LDA, DCTM demonstrates a much faster converging rate with better model fitting to the data. We empirically assess our approach using 268,231 scientific documents, from the year 1988 to 2005. Posterior inferences suggest that DCTM is useful for capturing topic and correlation dynamics, as well as predicting their trends.