The Gaussian functor associates to every orthogonal representation of a group G on a Hilbert space, a probability measure preserving action of G called a Gaussian action. This construction is a fundamental tool in ergodic theory and is the source of a large and interesting class of probability measure preserving actions. In this talk, based on a joint work with Yuki Arano and Yusuke Isono, I will present a generalization of the Gaussian functor which associates to every affine isometric action of G on a Hilbert space, a nonsingular Gaussian action. We thus obtain a new and large class of nonsingular actions whose properties are related in a very subtle way to the geometry of the original affine isometric action. In some cases, such as affine isometric actions comming from groups acting on trees, we show that a fascinating phase transition phenomenon occurs. By using nonsingular Gaussian actions, we also obtain a new dynamical characterization of Kazhdan's property (T).