The viscosity and diffusivities of silicate melts under high-pressure, high-temperature conditions are difficult to obtain experimentally. Estimation and extrapolation of transport coefficients are further complicated by their extreme sensitivity to melt composition. Our molecular-dynamics simulations show that, over a broad range of melt composition, temperature, and pressure, the diffusivities correlate with the excess entropy; approximations to the latter can be obtained from the knowledge of the radial distribution function. Using this structure-thermodynamics-dynamics relationship, we show that transport properties of silicate melts can be estimated quantitatively using static structure factor data from experiments.