Glad you asked. Yumeji's Theme. Nothing like plunked violin strings for percussion with the lone violin with melody. This song affectively is "in the mood for love". It expresses unrequited love, hope, and even mamihlapinatapai. So, I didn't mind sitting through the whole movie. The cinematography was great and it was a nice harmony to the music.
Of course, it also stars Tony Leung Chiu-Wai, who looks a lot like several of my uncles who were young adults in the 1940s. In fact, I wonder if this movie was picked up by the coffee babies because of him. Or is it because its a Kar Wai Wong movie?