While unimodal probability distributions are well understood in dimension 1, the same cannot be said in high dimension without imposing stronger conditions such as log-concavity. I will explain a new approach to proving confinement (e.g. variance upper bounds) for high-dimensional unimodal distributions which are not log-concave, based on an extension of Royen’s celebrated Gaussian correlation inequality. As the main application, I will deduce localization for random surface models with very general monotone potentials. Time permitting, I will also mention a related result on the effective mass of the Fröhlich Polaron with Rodrigo Bazaes, Chiranjib Mukherjee, and S.R.S. Varadhan.