Past Lives opens with a shot of three people sitting at a bar in New York — a man and a woman, both of Asian descent, chat with each other, while another man, who's white, looks silently on. We hear some people watchers offscreen casually wonder how these three are connected — are the Asian duo a couple, or are they siblings? Or is the white guy the Asian woman's boyfriend?

It's a nicely sardonic entry point into a story that's rooted in the writer-director Celine Song's personal experience. By the end of this exquisitely thoughtful and moving film, we've come to know and care deeply about all three of her characters, who are far more complicated than a snap judgment can convey.

After that prologue, the movie flashes back 24 years to when the two Asian leads were young classmates in Seoul, South Korea. The girl is named Na Young, and the boy is named Hae Sung. They're close friends, practically childhood sweethearts, but everything is about to change: Na Young and her family are immigrating to Canada, and she and a quietly heartbroken Hae Sung lose contact.

Twelve years pass. Na Young — now going by Nora, and played by Greta Lee — is a 24-year-old aspiring playwright in Toronto. Hae Sung, played by Teo Yoo, is an engineering student in Seoul. They reconnect by chance on Facebook and are soon spending hours video-chatting on Skype: Even though they haven't talked in more than a decade, the old bond is still there, maybe stronger than ever. But realizing that her renewed friendship with Hae Sung is distracting her from her life in Toronto, Nora decides they should cool it for a while.

It'll be another 12 years before they talk again, and by the time they do, Nora is living in New York and married to a fellow writer named Arthur — and yes, he's the white guy from the opening scene, played by John Magaro. One day Hae Sung tells Nora that he's coming to New York for a visit and would like to see her, sparking a conversation in which Arthur says, "the guy flew 13 hours to be here. I'm not going to tell you that you can't see him or something."

Nora and Hae Sung do meet a few times, visiting the Brooklyn Bridge and riding a ferry boat around the Statue of Liberty — a resonant image for this immigrant story. Their mix of sightseeing and soul-searching might remind you at times of Richard Linklater's Before trilogy, another talky, decades-spanning, continent-jumping love story.

Past Lives is both achingly romantic and earnestly philosophical. More than once Nora and Hae Sung use the Korean term inyun, a Buddhist-derived concept which suggests that every meeting between two souls is the product of countless interactions or near-interactions in their past lives. They muse about what might have happened if Nora — if Na Young — had stayed in Korea. Maybe she and Hae Sung would have gotten married. Or maybe not; maybe it's only because she left that their feelings for each other are so powerful now.

The two leads are wonderful. Greta Lee, from the series Russian Doll, reveals Nora's uncertainty but also her strength. She hints at both the confidence Nora's gained from her life as a successful artist and the identity confusion she sometimes experiences living in the West.

Teo Yoo is quietly heartbreaking as the more reserved Hae Sung, who's faced personal and professional disappointment back in Seoul and clearly longs for something with Nora that can probably never be. And the emotional stakes kick up several notches when Nora and Hae Sung go out one night with Arthur, bringing us to back to that scene in the bar. Magaro plays Arthur as a bit of a goofball, but also as a decent, understanding guy who at one point amusingly refers to himself as "the evil white American husband standing in the way of destiny."

What makes Past Lives so moving in the end is the grace that all three of these characters extend to one another in an awkward situation with no heroes or villains. You've seen the more conventional romantic-triangle version of this story, but Song isn't after melodrama; she wants us to see what's keeping Nora and Hae Sung apart, but also what's binding them, possibly for eternity.

Past Lives, which compresses two decades into barely two hours, is the most affecting love story I've seen in ages. It ends with a curiously hopeful image, focused less on the characters' past regrets and more on the infinite possibilities still ahead.