Japanese movie with similar plot (possible spoiler)

The Serendipity plot sounds a lot like a Japanese film I saw years ago. A young man and woman have great chemistry from the start, but they both think it's too good to be true, so they decide to part ways, yada yada. There may have been some time travel element or parallel universe element. I'd love to watch that movie again but I can't remember the name.

**Spoiler**




The boy and girl pass by each other in their future/alternate universe but don't recognize each other.