Mostly none, Im taking into account both Indian and Tibetan sources: When you regard Indian culture, its pretty confined to the indian subcontinent due to the geographics that make it so inexpugnable, and by always having a big population and strong religion that made invading civilizations almost a scratch on indian culture, the biggest indian cultural exchanges are probably with the greeks and after with the muslims. But thourgh Tibet it was almost impossible, the mountain range that is between them, the himalayas obveusly, its almost, for not saying impossible to get through, to find just a barren and huge steepe on the other side with barely no trade, no farming, resources, etc. Mostly indians only cared about india and it have never been an indian conqueror that took the conquest outside of india, and the culture follow up. Even the tibetans are extremely different from the Indiands, phisically, in language, in culture, even though they are not so far apart they are really close to mongolian and chineese culture than to indian. They aren't even the same ethnicity. So, no India never tried to conquer Tibet, and there was hardly any commmunications. Though, when the buddha came along by 500bc (source differ)
buddhism spread with the Mauryan dinasty and with it colonies in south east asia, that then started spreading through china. Buddism biggest centers of learning were in india so, buddist monks from china started making pilgrimages to India, but still they couldnt go straight they needed to go all they way through Tajikistan, Uzbekistan, Afganistan, Pakistan, and then India, but not connecting or passing by Tibet directly. That's why tibet remain fairly shamanic till 700AD when a King from tibet invited Gurú Rinpoché to taught them about buddism (by that time tibet was growing strong due to commerce between the silk road). But even so Tibet buddism was pretty similar to the chineese one and not the indian one. Then the Mongols took the buddism and adopt it from the Tibetans, so that's a "connection" between the steppe and india. But furthermore, there are no big influences noted in Indian history in commerce, culture, invasions, or art, refering any sign of Steppe or Tibetan culture. Yes, the kushans and the white huns where some of the few steppe conquests on India, but they were brief and not long lasting, and they didn't introduce any big cultural change. Mostly it is to blame the perfect enviroment that is India, sheltered by desert, jungles and the tallest mountain range in the world, and having all the human/farm/ores and resources required to strive. The only conection was buddism, but for India was only another sect and never went on to be more than 4% of their population. Their fighting, societies, organization, culture, food, art, temples, etc. doesn't seem to show any kind of Tibetan or Steppean influence

In early Indian literature China is invariably shown to be connected with India by a land-route across the country of the Kiratas in the mountainous regions of the north. In the Vanaparvan of the Mahabharata the Pandava brothers are said to have crossed the country of the Cinas in course of their trek through the Himalayan territory north of Badri and reached the realm of the Kirata king Subahu. The Cinas are brought into intimate relationship with the Himalayan people (Haimavatas) in the Sabhaparvan also. The land of the Haimavatas is undoubtedly the Himavantappadesa of the Pali texts, which has been identified with Tibet or Nepal. In the Sasanavamsa this region is stated to be Cinarattha. Thus, it is clear that China was known to the Indians as lying across the Himalayas and was accordingly included in the Himalayan territories. In the Nagarjunikonda inscription of Virapurusdatta, China (Cina) is said to be lying in the Himalayas beyond Cilata or Kirata. These references to the proximity of China to the Himalayan regions, inhabited by the Kiratas, show that there were regular routes through the Tibeto-Burman territories, along which the Indians could reach China.

Long before the northwestern routes were opened about the second century B.C. and long before the development of these Indianized states, there were two other routes from India to China. One of these began at Pataliputra (modern Patna), passed through Assam (Kamarupa of old) and Upper Burma near Bhamo, and proceeded over the mountains and across the river valleys to Yunnanfu (Kunming), the main city of the southern province of China. The other route lay through Nepal and Tibet, was developed much later in the middle of the seventh century when Tibet had accepted Buddhism.