A model is presented to predict the depression of the glass transition temperature of a polymer in the presence of a liquid, gas, or supercritical fluid as a function of pressure. It is developed using lattice fluid theory and the Gibbs-Di Marzio criterion, which states that the entropy is zero at the glass transition. Four fundamental types of T(g) versus pressure behavior are identified and interpreted as a function of three factors: the solubility of the compressed fluid in the polymer, the flexibility of the polymer molecule, and the critical temperature of the pure fluid. A new phenomenon is predicted where a liquid to glass transition occurs with increasing temperature, which we define as retrograde vitrification. This retrograde behavior is a consequence of the complex effects of temperature and pressure on sorption. For the limited data which are available for the polystyrene-CO2 and poly(methyl methacrylate)-CO2 SYStems, the predictions of the model are in good agreement with experiment.