In ancient times, the Chinese looked on India at the home of Buddha and the source of Buddhism. Many Chinese pilgrims came to India to study at Taxila and Nalanda University. Indian Buddhist monks also traveled to China, where they were much respected.

Fa-Hien (Faxian) was among the Chinese pilgrims who traveled to India in search of Buddhist scriptures, to Gandhara and Peshawar, which were centers of Buddhist learning at the time (4th century AD). He wrote a book "Travels of Fa-Hien" in which he described his visit to India in great detail.

Another noted Chinese traveler was Hsuan Tsang, who visited India in the 7th century and lived there for 14 years. He studied at Nalanda University for 5 years. Like many other Chinese scholars, he was unhappy with the quality of Buddhist texts available in China, and traveled to India to study Buddhism at its source. He also wrote several texts about his journey to India, and he also brought back 600+ Buddhist texts back with him from India, which he translated.

Unlike Europe, it was close enough for regular contact

But it really wasn't. Although the geographical distance between India and China isn't large, there is a substantial barrier along the way, the Himalayas. Contacts between China and India have always been difficult for this reason, and while really dedicated people such as religious pilgrims have made the trip, there was never much intermixing of populations.

For example, Hsuan Tsang took the western route, through the Tarim Basin, Turfan, Tashkent and Samarkand, through Bactria into Afghanistan and through the Khyber Pass into India. This journey is thousands of miles through very difficult terrain. Another way would be via the east, but then you have to cross the jungles of Burma and Assam, which were full of warlike tribes (some of them headhunters) to get through. There is another route via the Tibetan plateau, but it's also very difficult and besides, Tibet was independent for most of history, a buffer state between India and China.