The best of intentions can’t rescue a relationship that has run its course, a lesson learned through tears, small explosions and passionless embraces by Dean and Cindy, a young married couple watching the embers of their romance turn cold in Blue Valentine.

As is often the case in a union soured by time and subtle estrangements, neither husband nor wife seems eager to admit that their marriage has been reduced to a tenuous living arrangement, maintained mostly for the benefit of their 6-year-old daughter, Frankie (Faith Wladyka). Dean (Ryan Gosling) pretends not to notice, afraid to ask the hard questions that Cindy’s ambivalence begs.

Cindy (Michelle Williams), for her part, has already checked out, committing her time and energy to her work as a nurse. Once, in a lifetime far removed from the demoralizing humdrum her days have become, she dreamed of becoming a doctor. Now that hope is dead, and her patience with Dean, a shiftless house painter who aspires only to be a loving father and husband, has worn perilously thin.

Dean senses this, but rather than opening a dialogue that might mean the end of his family, he coaxes Cindy into a romantic weekend at a cheap motel. Their choice of accommodations: Cupid’s Cove or the Future Room. Dean opts for the Future — a dark, windowless cave adorned with cheesy sci-fi affectations, an appropriately grim setting for a failed attempt at making love.

Even as they play out the string of a flatlining romance, it’s easy to imagine Dean and Cindy in happier times. Early on, quite without warning, director Derek Cianfrance, who co-wrote Valentine with Joey Curtis and Cami Delavigne, returns us to the kindling glow of their courtship, through a series of flashbacks standing in stark contrast to the ominous clouds hanging over the rest of his movie.

We see lovers lost in the heady intimacy of mutual attraction — younger, leaner and powerless to resist each other’s charms, which are genuine enough. (The movie’s dialogue was largely improvised by Gosling and Williams, who seem marvelously unaffected throughout.) Where did the passion go? What, in six short years, turned their joy to apathy?

Cianfrance leaves such questions to our imagination, and anyone who has watched love dissipate into thinly veiled contempt can fill in the blanks. That Dean and Cindy stay civil for so long, their life together a slow, agonizing death march mostly devoid of melodrama — with riveting performances by Gosling and Williams, laying themselves bare, emotionally and physically — gives Valentine its withering power.