Now that Alain Resnais has died, Jim Jarmusch should inherit the title of Major Auteur With the Coolest Hair. A snow-white mop with a wild streak and neat sideburns ending at the earlobes, his coiffure could be the snug hat for a Russian princess. Jarmusch, 61, is pretty hip too. A writer-director of truly, incorrigibly independent films — not “indie,” which he’s said “has been usurped as a marketing device” — he is also one of three members of the music project SQÜRL, which he describes as “an enthusiastically marginal rock band from New York City who like big drums & broken guitars, cassette recorders, loops, feedback, sad country songs, molten stoner core, chopped & screwed hip-hop, and imaginary movie scores.”

So there might be a dab of self-portraiture in the character of Adam (Tom Hiddleston) — a retired rock star with fabulous hair and a love for all things classic — in Jarmusch’s divinely decadent Only Lovers Left Alive. Adam dwells in seclusion in his louche Detroit mansion, buys vintage electric guitars from his friend Ian (Anton Yelchin) and gets his drug of choice from the local hospital’s helpful “Dr. Watson” (Jeffrey Wright). His glamorous wife Eve (Tilda Swinton) often visits him from her home in far-off Tangier to rekindle their longtime love. Looking great for their advanced age, Adam and Eve are handsome, swank and in love. They’re also vampires.

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For a director who has delved into the preternatural and postmortem in Mystery Train, Dead Man and Ghost Dog: The Way of the Samurai, it might be a mission of mercy to rescue the creatures of the night from the teen vamps of The Twilight Saga and Warm Bodies. But Only Lovers Left Live is also, and mainly a romance about, sexy old people. At least 2,000 years old: Adam and Eve are bimillennarians, and then some. Could they be the original Adam and Eve? If so, in this retelling of Genesis, the first family is undead and the bloodline has been sadly diluted. Vampires are the elite, a chic minority in a world overrun by zombie rabble; Ian is one of those, nicer than most but considerably subordinate in power and majesty to Adam.

Only Lovers Left Alive also has reverberations of Michael Haneke’s Cannes winner and Oscar nominee Amour, about a married, music-loving couple of octogenarians and the younger family member who pesters them. Instead of the middle-aged daughter in Amour, it’s Eve’s kid sister Ava (Mia Wasikowska), sporting all the recklessness of youth — after all, she’s only, like, 300 years old. She guzzles Adam’s precious supply of O-negative blood, totals his heirlooms and gets a little too frisky with Ian. As Eve noncommittally remarks after the zombie’s body melts in acid, “That was visual.” Adam, a J.D. Salinger among rock artists, is furious when Ava plays one of his recent compositions at a nightclub, but he tolerates his kid sister-in-law with the observation, “Families are always a bit weird.”

(READ: Mia Wasikowska, the heir to Jane Eyre)

In images captured by cinematographer Yorick Le Sax (who also photographed Swinton in Julia and I Am Love), the streets of Tangier swirl with moody mystery, and the low lights in Adam’s Motor City pad pick up glimmers of shiny guitars among the murk and detritus. “I do find romantic appeal in desolation and postindustrial landscapes,” Jarmusch has said. “Detroit is a depopulated ghost town, and Tangier is a crumbling place that’s full of life.” In Mediterranean Morocco, Eve pals around with the vampire Christopher Marlowe (John Hurt), who is still annoyed that the credit for his plays went to Shakespeare — “That illiterate zombie!” — and who wishes that 400 or so years earlier he had known Adam, who would have made a perfect model for Marlowe’s Hamlet.

The wry comedy is filigree work around this romantic tale of two souls who share the purest, deepest, sexiest, most affectionate love of any twosome in modern movies. They swan through the film like ancient rock royalty, gracing discos and jetting to exotic locations. Adam is an immortal flirting with suicide (he needs a wooden bullet), while Eve is attuned to the changing of the seasons (so many in her time on earth). But this aging couple is in total emotional and devotional synch. They evoke such classic tandems as Nick and Nora, Noël and Gertie and Gomez and Morticia, with a little Sid and Nancy for spice.

(READ: Why Tilda Swinton is the Queen of the Indies)

In the 21st century, most vampires don’t sup on human victims — consider the contagions they might pick up — but acquire their blood supply through friends and unscrupulous medicos. All that shopping must weary Adam, frustrated that he is deprived of death. But Eve is the ideal antidote to depression, telling her spouse that things like “appreciating nature” and “kindness and dancing” make life worth living for the undead. And so they dance at home to Denise LaSalle’s “Trapped by a Thing Called Love.” As Adam hardly needs reminding, he’s been “lucky in love.”

Hiddleston, known to Marvel fans as the brooding, maleficent Loki in the Thor and Avengers movies, stepped into the Adam role when Michael Fassbender stepped out. Nothing against Fassbender, but Hiddleston is a wonderful partner for Swinton, in her first Jarmusch lead role after guest appearances in Coffee and Cigarettes and The Limits of Control. Tall, slim aristocrats with matching cello voices and feral manes (makeup designer Gerd Zeiss gave them yak and goat hair), they embody an older, graver, more graceful species, dancing to a score — including music by SQÜRL — that turns dirges into the sublimest ballads.

(READ: Corliss on Tom Hiddleston in Thor: The Dark World)

Swinton has been the towering, liberating muse of many a director, including Jarmusch. “One of the great moments in my life,” he told David Ehrlich of the Guardian, “was when we were shooting The Limits of Control, and we finished a take and I said: ‘Oh Tilda, that was so beautiful, will you marry me?’ And she replied: ‘Oh darling, we already are.’ I could have died.”

That anecdote expanded, with Jarmusch as Adam, could be this swooning movie. But died? Never. Less a drama than a miniature double portrait, Only Lovers Left Alive creates two people whose joy, not pain, is to be together forever. C’est l’amour.

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