It, however, postulates the question that, how would the world (yes, not just India) be different had the Tang vassalized the many Indian states and asserted Chinese cultural hegemony, effectively bringing it into the Sinosphere?
Note--later, they do rule independent states, but they still take cultural cues from China
The Beginnings: Tang Era
In the mid-Tang era, Chinese scholars and officials (often inseperably connected) became increasingly fixated on India as a disunified nation which had lost Buddhism, its cultural contribution to China, ripe to be re"civilized" under Chinese rule. As Buddhism grows in influence, China looks upon India as uncivilized, lacking in what made it great. However, not all are swayed by this new influence, and it is agreed to send diplomats to Kashmir as well as the Northeastern Indian states. Being seemingly rebuffed (translations caused misunderstanding), China took this as an opportunity to conquer India
Around 750 CE, the Tang decided to invade Kashmir and Assam. Both invasions were successes, and so, inspired, the Chinese attacked further, moving into Bengal and the Thar Desert. There were many small states in India, so instead of further military conquest, the Tang preferred to plant agents into governments that allowed China to gain political power. By 775, these political ties had grown to become a complex set of alliances which China used to vassalize and subjugate most of North India in a matter of a few years and small, decisive conflicts. These were handled by a legendary foreign minister who was able to easily maneuver alliances by making and breaking them through political pressure.