As in the 2005kz R band example, the GPs propagate the lightcurve continuing the latest trend in the data. If the last 2 datapoints indicate brightening, the GPs allow the lightcurve to get brighter thereafter. This is a problem with the data, not iwth the GPs, that cannot be solved in a non-parametric fashion, without imposing strict constraints on the sign of the derivative, but that in turn would not allow us to characterize individual peculiarities in SN lightcurve behavior.