In the study of K-stability, one crucial problem is to show the graded algebras associated with certain valuations are finitely generated. For a class of "special valuations", such finite generation theorems were first proved by Liu-Xu-Zhuang for Fano varieties and by Xu-Zhuang for klt singularities. In this talk, I will explain a new proof by studying the extended Rees algebra directly. This new method allows us to extend the finite generation to a larger class of valuations, and provides some extra information on the associated graded algebras.