Although there is no diffuse groundwater recharge at many semiarid sites, evidence for diffuse recharge exists at some locations where mean annual precipitation $overline{P}$ is much less than mean annual potential evapotranspiration $overline{PET}$, particularly where soils are coarse and rainfall variable is substantial. We investigate the climatic controls on diffuse recharge using a one-dimensional, variably saturated flow model. The model is driven by a stochastic parameterization of climate that includes storm size distribution and seasonality of precipitation (P) and potential evapotranspiration (PET), constrained by data from 536 weather stations in the southwestern United States. Storm size distribution and seasonality determine the frequency and duration of intervals when P exceeds PET, which controls the flux of water past the root zone. For coarse soils, climates with large, infrequent storms yield recharge when $overline{P}$/$overline{PET}$ exceeds 0.4, compared with 0.7 for a typical climate. Recharge through fine soils is insensitive to storm size and occurs at $overline{P}$/$overline{PET}$ > 0.8. Seasonality has a stronger influence on recharge than storm size distribution, and the effects are similar for coarse and fine soils. Recharge is relatively insensitive to rainfall seasonality. In contrast, the typical PET annual cycle lowers $overline{P}$/$overline{PET}$ of the recharge threshold by 0.3. The relative timing of P and PET maxima is critical: Recharge occurs at $overline{P}$/$overline{PET}$ values that are lower by 0.2 when the rainy season occurs during winter instead of summer. Over the range of climate and soils examined, $overline{P}$/$overline{PET}$ values at the recharge threshold varied from 0.2 to 0.7. Therefore $overline{P}$ and $overline{PET}$ alone are insufficient to predict where recharge will occur.