Downscaling aims to link the behaviour of the atmosphere at fine scales to properties measurable at coarser scales, and has the potential to provide high resolution information at a lower computational and storage cost than numerical simulation alone. This is especially appealing for targeting convective scales, which are at the edge of what is possible to simulate operationally. Since convective scale weather has a high degree of independence from larger scales, a generative approach is essential. I will describe a statistical method for downscaling moist variables to convective scales using conditional Gaussian random fields, with an application to wet bulb potential temperature (WBPT) data over the UK. This model uses an adaptive covariance estimation to capture the variable spatial properties at convective scales.