It is shown that mathematical and empirical relationships which exist between chemical potential gradients and diffusion coefficients for a multicomponent system may be used to estimate or constrain the magnitudes of various parameters in macroscopic thermodynamic mixing models. Illustrations of the approach are provided using data on silicate melts. When the mixing behavior is well-known, the same relationships may be utilized to constrain unknown diffusion parameters. These relationships may be particularly useful in estimating temperature and pressure dependences of mixing parameters.