Mass transport controls both materials processing and properties, such as ionic conductivity, in a wide variety of materials. While first-principles methods compute activated state energies, upscaling to mesoscale mobilities requires the solution of the master equation. For all but the simplest cases of interstitial diffusivity, calculating diffusivity directly is a challenge. Traditionally, modeling has taken two paths: uncontrolled approximations that map the problem onto a simpler (solved) problem, or a stochastic method like kinetic Monte Carlo, which is difficult to converge for strong correlations. Moreover, uncertainty quantification or derivatives of transport coefficients are complicated without analytic or semianalytic solutions. An automated Green function approach for transport both determines the minimum set of transition states to calculate from symmetry and computes the dilute-limit transport without additional approximations. We consider different systems to showcase the flexibility and accuracy of the approach: solutes in magnesium alloys, zirconium alloys, and complex oxides.