Stable isotope data from hydrothermally altered rocks often show significant scatter. Such scatter cannot be quantitatively interpreted by models in which each lithologic unit is assumed to have a uniform permeability. If a stochastic modeling approach is used instead, heterogeneous permeability maps can be constructed to approximate the statistical distributions of natural systems, and both overall isotopic trends and data scatter can be matched. Three models are presented for the Alta, Utah, contact aureole to show that the observed scatter in δ18O values is consistent with subhorizontal down-temperature fluid infiltration through carbonates with heterogeneous permeabilities. Infiltration through rocks with heterogeneous permeabilities creates irregular, lobate isotope patterns, so that the idealized isotope profiles predicted by one-dimensional homogeneous permeability models do not develop. Localized sampling is unlikely to yield an accurate estimate of the overall importance of fluid-rock interaction or of dominant flow directions. In heterogeneous systems, large-scale hydrothermal alteration and flow patterns can best be estimated from statistically unbiased and spatially distributed data sets.