SECRET SUNSHINE: Jeon Do-yeon’s performance shatters genre conventions.

Perhaps the most readily categorized of the three I saw is GREEN FISH (1997; May 4 at 3 pm), a gangster flick whose pattern can be recognized in Martin Scorsese movies ranging from Mean Streets to The Departed. It opens with an exquisite image: a young man (Han Suk-kyu) on a train spots a woman in a fuchsia scarf leaning into the wind. The scarf blows off and into his face — covering the camera lens. The woman becomes his obsession, the scarf distorting his perceptions. She’s the abused moll of a Seoul gangster, and the smitten hero becomes one of the gangster’s lackeys. So far the story arc is plain, but dragging it down is the young man’s past — his impoverished family, who’ve been discarded by a heartless society, and his dream to gather them together again.

In PEPPERMINT CANDY (1999; May 3 at 7 pm), the genre is the cop thriller, but it takes some reverse exposition to get there. The candy of the title is the tea and madeleine of Yongho (Sol Kyung-gu), his and the viewer’s Proustian guide as he regresses into the past from a present in which he’s a failed middle-aged businessman about to be squashed by an onrushing train. What brought him to commit suicide in the midst of a 20th-anniversary get-together of long-forgotten friends? Introduced by the image of a train running backward, episodes from Yongho’s — and South Korea’s — past tell his tale in reverse.

It begins in small-town naiveté and first love that is brutalized by a stint in the army in 1980, when the country has been plunged into military rule. Thus hardened, Yongho becomes a detective, and the film tries to organize itself into the appropriate genre. But police work seems to consist of torturing political prisoners, getting drunk, and singing karaoke, and the film breaks down into melodrama on the brink of hysteria. Since he comes off as an unrepentant pig, Yongho’s extreme emotions don’t arouse much sympathy till the very end, when the film returns to the site of its opening scenes, but two decades earlier, and Yongho, his innocence yet to be corrupted, experiences a moment of déjà vu and tragic clarity.

Like Peppermint Candy, SECRET SUNSHINE (2007; May 2 at 7 pm) also flirts with melodrama before the generic wheels start to fly off. The title — Milyang in Korean — is the name of the small town where Shin-ae (Jeon Do-yeon) has relocated from Seoul with her little boy. Her husband, who’s been killed in an accident, was born there, and Shin-ae wants to honor his memory and start her own life anew.

Her plan goes awry from the start when her car breaks down on the outskirts of town. The mechanic who fixes it starts to stalk her. Neighbors gossip and ostracize her as uppity and strange, and when tragedy strikes again, she’s seduced by a predatory cult of born-again Christians. But her needs and unrestrained emotions overwhelm not only socially acceptable outlets but also the complacent conventions of melodrama. With a shattering performance by Jeon Do-yeon, Lee’s film joins the ranks of Krzysztof Kieslowski’s Bleu|Blue and Lars von Trier’s Breaking the Waves as an unforgettable depiction of rage, loss, and grief.