Efforts to construct predictive grain boundary (GB) structure-property models have historically relied on property measurements or calculations made on bicrystals. Experimental bicrystals can be difficult or expensive to fabricate, and computational constraints limit atomistic bicrystal simulations to high-symmetry GBs (i.e., those with small enough GB periodicity). Although the use of bicrystal property data to construct GB structure-property models is more direct, in many experimental situations the only type of data available may be measurements of the effective properties of polycrystals. In this work, we investigate the possibility of inferring GB structure-property models from measurements of the homogenized effective properties of polycrystals when the form of the structure-property model is unknown. We present an idealized case study in which GB structure-property models for diffusivity are inferred from noisy simulation results of two-dimensional microstructures, under the assumption that the number of polycrystal measurements available is larger than the number of parameters in the inferred model. We also demonstrate how uncertainty quantification for the inferred structure-property models is easily performed within this framework.