How did buddha-nature thought develop?

The theory of buddha-nature (tathāgatagarbha, for the most part)--that all sentient beings somehow possess the innate buddhahood or potential to become buddhas and (sometimes by extension) that therefore all of reality shares in the same fundamental essence--seems to have appeared in India in as early as the Second Century CE before spreading to China and Tibet and beyond. Since the early days of the religion Buddhists have been disagreeing about whether the true nature of reality can be described in positive terms or must always be couched in negations, a debate that is reflected in the early-Buddhist focus on nirvāṇa and the extinquishing of the stuff of saṃsāra, or later Buddhist emphasis on enlightenment and the actualization of a universal all-pervading truth. Scholars mostly now agree that buddha-nature theory developed alongside--rather than part of--the two main Indian Mayāyāna Buddhist doctrinal schools of Madhyamaka and Yogācāra, and great thinkers of each have both embraced it and rejected elements of the teaching. Over the centuries buddha-nature has been interpreted as a definitive teaching, as a provisional teaching, or as not Buddhist (most recently in the form of Critical Buddhism in Japan) and although it is interpreted in different ways, buddha-nature has become a central element of Buddhist doctrine in all Mahāyāna traditions.