As Buddhism in China developed its own distinctive tendencies, the belief in Buddha-nature, resonating with the indigenous East Asian essence-function 體用 paradigm, became a central tenet in the majority of surviving influential schools, including Tiantai 天台宗, Huayan 華嚴宗, Chan 禪宗, Pure Land 淨土宗, and the various Lotus-related schools. The Faxiang school 法相宗, however, representing East Asian Yogâcāra, did not teach a doctrine of innate Buddhahood. There were also differences in terms of interpretation of the process of actualization, with doctrinal/gradualist-oriented schools emphasizing the necessity for uncovering the pure nature through continued practice, while certain suddenist traditions emphasized that the buddha-nature is already fully manifest in everyone, just as they are.

References:

Ruegg, David Seyfort. 1989. Buddha Nature, Mind and the Problem of Gradualism in a Comparative Perspective: On the Transmission and Reception of Buddhism in India and Tibet. London:  School of Oriental and African Studies, Univ. of London.

Zimmermann, Michael. 2002. A Buddha Within: The Tathāgatagarbha Sutra: The Earliest Exposition of the Buddha-Nature Teaching in India. Tokyo:  The International Research Institute for Advanced Buddhology, Soka University.