A generic molecular thermodynamic model is developed for linear and branched polymer solutions in a cubic lattice. The long-range correlations beyond the nearest-neighbor interaction sites are incorporated, which account for arbitrary coordination number of lattice and arbitrary degree of branching. A significant improvement is found from our model over Flory-Huggins theory and lattice-cluster theory in the predictions of phase equilibria. The model correctly predicts a reduced critical temperature, an increased critical composition, and a lower miscibility with enhanced degree of branching, as observed in simulation and experimental studies. The model also satisfactorily predicts the phase behavior of branched polystyrenes with different molecular weights and architectures in cyclohexane. (c) 2006 Elsevier B.V. All rights reserved.