Diffusion is a fundamental phenomenon resulting from stochastic processes, giving rise to a wide range of natural phenomena and determine essential manufacturing processes, with some of the most critical ones being the smoothness of semiconductor heterostructure interfaces such as p-n junctions and dopant diffusion for Fermi level shifting in electronic devices. In this thesis, we study diffusion starting from a discrete microscopic master equation to develop a rigorous framework for diffusion modeling. We begin by generalizing the procedures used to obtain coarse-grained diffusion equations from master equations, showing how ideal free energy contributions can be accounted for in a mathematically stable manner. We then consider the rigorous formulation of free energy as a driving force, developing a unified theory of free energy functionals that reduces to the Ginzburg Landau free energy in the appropriate limits, and investigate numerically how the Cahn-Hilliard free energy and a generalization of gradient energy theories behave for systems with constant diffusivity. Finally, based on a rigorous formulation of multicomponent interdiffusion, we develop a coarse-grained Kinetic Monte Carlo method as another approach for simulating the master equation dynamics, and explicitly discuss the assumptions in point defect mediated interdiffusion modeling that are needed for this framework to be valid.