For valuations with a rational rank larger than one, the finite generation of its associated ring is a question beyond the classical minimal model program. Nevertheless, it plays a key role in K-stability theory of Fano varieties. In this talk, I will discuss our proof of finite generation for valuations which are on a special dlt model, and its application to optimal destabilization in K-stability theory. The talk is based on joint works with Yuchen Liu, Ziquan Zhuang.