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 semi-analytic solutions. A new 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 compute diffusivity in a variety of systems to showcase the flexibility and accuracy of the approach.