I can't comment on Rome formally, but Indian art, especially in the northwest, near what was known as Bactria (in modern day Afghanistan) had a strong Greek influence. Alexander the Great's conquest of the region installed Hellenic influences in the area, resulting in a Hellenized-Buddhist synthesis that spread through the mountains known as the Hindu Kush into modern-day Pakistan and the Punjab. Later, the Kushans, a tribe of the Yuezhi people that originated from modern-day Kyrgizstan/Uighurstan(Xinjiang), conquered the area, and adopted a synthesis of Greek and Buddhist motifs in their culture, eventually spreading this Buddhism to China and eventually Korea and Japan.

For comparison, here's a Buddha in the Hellenic style and one in the Japanese style. Notice how the first one employs some classical Hellenistic motifs, as compared to this statue.

I should also add that Roman art also derived from the Hellenic tradition, so one can see similarities between Roman art and some of this Greco-Buddhist art, because they do share some common roots.