In the 1950s, Yano and Nagano proved that the round sphere is the only complete Einstein manifold admitting a one-parameter family of conformal transformations. Since then, a number of results have been discovered regarding conformal diffeomorphisms of Einstein spaces. I will discuss recent work with William Wylie in which we extend these theorems to generalized quasi-Einstein (GQE) manifolds, a class of spaces that includes gradient Ricci solitons and static metrics. We also prove sharp characterizations of conformal transformations between shrinking and steady gradient Ricci solitons to other solitons. As with the classical results, we assume the conformal diffeomorphisms are non-homothetic, and we additionally assume the potential function is preserved up to a constant.