The Wikipedia article on Buddhism in Iran suggests that, even with persecution from the Persian government, Buddhism was fairly widespread in Central Asia and within Persia itself before the spread of Islam. So, what would be the best point of divergence to make Buddhism the official and/or majority religion in the empire? What would the local variety of Buddhism look like in such a scenario, especially considering the Abrahamic and Zoroastrian influences in the region? How would a Buddhist Persia interact with the Roman Empire, especially if Rome still adopts Christianity? What about the relationship between Persia and other nearby powers?