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AI weather models now rival physics-based models on grid-scale scores, but their rainfall is a grid-box average, not the rain a gauge receives. We adapt the discrete Gaussian model of geostatistical change of support into a post-processor that converts a 0.25° forecast into a point rainfall distribution. The latent correlation r between a point and its grid box is derived from the gauge correlogram alone, and one fitted parameter, the forecast-to-block correlation ρ, measures forecast skill. We verify GraphCast and ECMWF HRES day-1 to day-3 forecasts and ERA5 against 686 337 gauge-days at 1984 sites in Iowa, Illinois, and Missouri during 2020, using leave-one-month-out cross-validation. The method raises GraphCast day-1 continuous ranked probability skill from 0.04 to 0.38 and restores the observed frequency of days with at least 50 mm. With one fitted parameter it comes within 1.7% of a five-parameter censored shifted gamma regression and a binned empirical method for GraphCast; for HRES it matches the regression and doubles its 50-mm Brier skill. The correlogram-derived r adds significant skill over a constant coefficient. Point skill separates into representativeness, with r falling from 0.97 in autumn to 0.90 in August, and a forecast-to-block correlation that is nearly constant through the year (0.86 for GraphCast and 0.84 for HRES at day 1). After post-processing, ERA5-initialized GraphCast outperforms HRES at all leads. Because r needs only gauges, the method is interpretable and transferable.