South Asia:
A clear example is India's languages. In India, English is spoken, although it is a Saxon language from a completely different part of the world, as in, from a different continent, a different culture and has different roots. The colonization of India was what caused this and many other things to be assimilated by Indians and, most of the times, those things were imposed.
At least, Speaking English was eventually helpful to Indians and assimilating part of the British culture helped, even though just a little, the country to be a little better developed.
East Asia:
The most common cultural diffusion in East Asia is how the Ideograms used by the Chinese are used also in other countries. In Japan, they have its own name, Kanji, but they serve mostly the same purpose. Koreans have also used those same characters for a long time. This all happened, most likely, because of China's influence on other cultures and how they were, in a way, originated in it. The Chinese system was the first in the region to be created and therefore the only one used for a long time.
Eventually, for having a very complicated way of writing things, the solution that the Koreans came out was to create a simpler new way of writing for the common folk to be able to read. Nowadays, the Koreans have their own characters and they are much more practical and easier than the Chinese one.
Southeast Asia:
The countries in southeast Asia have a closely interrelated history and it works the same way for their culture, which was shaped by the passage of many other cultures and religions that came with old trade routes. Being between the economic demands of the Chinese and Roman Empires, countries like of Vietnam, Indonesia, Thailand, Laos, and Malaysia ended up being frequently, and more and more exposed to new cultures from the west and the east, which eventually had a significant effect on their artistic traditions.