In his Oscar-winning “Ida,” Polish writer-director Pawel Pawlikowski offered an emotionally devastating commentary on his country’s history during World War II and its communist aftermath through the story of a young postulant who leaves a Catholic convent in search of her past. His new film also confronts the grim reality of Poland’s post-war experience, but does so by following an intimate relationship as tempestuous as the titular standoff between the eastern and western blocks against which the story is set. (Reportedly his script was inspired by his own parents’ stormy marriage.)

The plot is, in purely narrative terms, a very simple one. In 1949 world-weary musician Wiktor (Tomasz Kot) and his acerbic partner Irena (Agata Kulesza) are being taken around the countryside by a bumptious driver named Kaczmarek (Borys Szyc). Their effort may have originated in a quest to preserve endangered folk-music forms, but it turns into a government-supported enterprise to audition local talent for a troupe of folk singer-dancers, an ensemble that can present national culture to the world—and, of course, serve as a propaganda tool for the socialist regime.

One of the young ladies they encounter is a spitfire named Zula (Joanna Kulig), who might not have the purest voice in the world, and will have to be taught to dance properly, but whose vibrant personality marks her as a prospective star. Wiktor chooses her for placement in their new school, despite Agata’s misgivings, and soon he and his protégé are passionately in love.

The film follows the relationship over the course of decades as it burns hot and cold, just as the reality between east-west does. The troupe gains recognition in Eastern Europe and the Soviet Union itself, and eventually is employed as a political tool in the west as well. Its success makes the career of Kaczmarek, who becomes the manager and compliantly follows the orders of his government superiors.

But the lovers, while both yearning to break free of rigid control from above, can never shed their selfish needs. Each suspects the other of betraying their secrets to Kaczmarek, and not without cause. Moments of utter commitment alternate with angrily accusatory outbursts and ruptures, until, when they hastily plan escape to the west, Zulu decides not to go through with it, leaving Wiktor to make a life for himself as a solitary exile.

But that does not end things. Wiktor will travel to Yugoslavia to see her again, endangering himself in the process (indeed, he does fall under scrutiny of the security services, and there is a chance he will wind up in the USSR). Zula eventually finds her way to Paris and reunites with Wiktor, and the old passion is reignited, though so too is their habit of hurting one another. It is, in effect, the apparently universal tale of a man and a woman who can’t live with one another, but can’t endure being apart; it’s just that in this case it’s played out on both sides of the iron curtain as the world is changing.

“Cold War” is a challenging work, marked by abrupt time shifts and narrative ellipses fashioned by Pawlikowski and editor Jaroslaw Kamiński that the viewer must work to understand, but it’s made with exquisite care, just as “Ida” was. Shot by cinematographer Łukasz Żal, as the earlier film was, in black-and-white and the boxy Academy ratio, the images are subtly composed, but designed for emotional as much as visual impact, with changes in contrast mirroring those of mood. Equally important is the extraordinarily eclectic score, which ranges from folk numbers and Stalin-era proletarian pieces to jazz, western popular songs and snatches of Bach; it too reflects the mercurial inner lives of Wiktor and Zula.

So do the intense performances of Kulig and Kot, who hold little, if anything, back in conveying the lovers’ radical swings. Hers is the splashier turn, since Zula is the utterly extroverted part of the pair, but Kot anchors things with his more studied, somber approach. And while Kulesza doesn’t get as much opportunity as you might wish to express Irena’s cynicism, Szyc paints an incisive portrait of a bland apparatchik who makes the most of the chances for advancement that come his way.

Pawlikowski’s film is a brilliantly melancholy portrayal of two people who can’t resist one another but are doomed to destroy their chance of enduring happiness, as well as the oppressive system they’re trapped in.