Like his countryman Chan-wook, the Korean director Kim Ki-duk willfully divides audiences and probably gets hit back harder than he deserves. His simple, disarming parables please some and provoke others, though he has shown signs of scaling back the violence that more generally ruffle feathers. Two of his recent films to see American releases — the pseudo-Buddhist “Spring, Summer, Fall, Winter … and Spring” and the ersatz Tsai Mingliang fable “3-Iron” — could be downright sweet (or, again, fatuous, depending whom you asked).

The plastic-surgery anti-romance “Time” is not going to resolve the debate. This is partly because Mr. Kim falls back on his bad habit of crafting female characters to convey simplistic psychosexual lessons, and partly because he’s chosen strident forms that keep pushing us away. The best way to take “Time,” in which a jealous shrew abruptly quits her boyfriend and resculpts her face to return as a different person, is as a melodrama spiked by horror-inflected revelation, rather than as a ham-handed, weakly acted drama.

But that necessitates discarding swaths of a film that hover around the memory of a shallow, barely sketched relationship. One day, insecure Seh-hee (Ji-yeon Park) runs out on her dull boyfriend, Ji-woo (Jung-woo Ha), without a word, some time after baiting the distracted but committed fellow with a thin-skinned tantrum. In the ensuing months, the dazed Jiwoo feebly goes through the motions of dating again but keeps getting reminded of the past.

Then, at his favorite café, a forthright waitress suspiciously named See-hee (Hyeon-a Song) reels him in and knocks him back into uncertainty. This apparent return of Seh-hee in her new guise triggers, irony of ironies, Jiwoo’s tortured loyalty to the old relationship. After some confusing courtship, Ji-woo’s ultimate reaction, no less extreme than See-hee’s, brings the film full circle with another fresh reversal.

As Mr. Kim puts his hard-to-like characters through their paces, he occasionally demonstrates his cinematic flair for finding scenes that engage as immediately and unself-consciously as a game might. One such scene really is a game: On a ferry, Ji-woo kicks a soccer ball back and forth with a mysterious woman whose face is obscured. Just when he’s really getting into it, and when he might suspect her of being See-hee, she disappears between volleys.

More often than not, “Time” is hobbled because we feel we have little stake in the couple’s reconciliation. Mr. Kim flashes a welcome sense of humor about their plight, and how the young characters harangue each other, but it only underlines the shrillness of the sentiments. A hideously trite sculpture garden that the movie revisits, featuring bodies in various poses of entanglement and repose, encapsulates how “Time” gets stuck on Mr. Kim’s first premise.

But “Time” does yield a gut-level catharsis that leaps past the particular woes of this couple, as well as Mr. Kim’s obligatory commentary on the superficial art of plastic surgery. When one character appears wearing a mask of her own face, looking creepy and clownish, the movie flames out gloriously with the sense of how lost love can unmoor the afflicted, and how trying to recreate what is lost compounds the folly. Mr. Kim cleverly holds back information here and there, putting us in the shoes of a lover desperately seeking the comforting recognition of the familiar.

Until that conclusion, “Time” is largely wasted, despite the portentous title and the promising influence of Hiroshi Teshigahara’s 1966 transplant classic “Face of Another.” (There’s also a reference to Buñuel’s metaphysical double date “That Obscure Object of Desire,” which featured two actresses playing the same character.) Mr. Kim has fortunately abandoned the precious dialogue-free approach that bottomed out with 2005’s “The Bow,” but as “Time” shows, he’ll need a better way of expressing what he says.