Coarse master equations and diffusion models provide powerful tools to study the equilibrium and non-equilibrium properties of molecular systems. Maximum likelihood and Bayesian approaches have been used successfully to construct such models from the observed dynamics projected onto discrete and continuous low-dimensional sub-spaces. By using a Green's-function based formalism, issues arising from fast non-Markovian dynamics can be circumvented. The general formalism for the construction of coarse master equations and diffusion models will be illustrated with applications to peptide and protein folding.