“Love is not a victory march,” Leonard Cohen sang in one of the many verses of his signature song “Hallelujah” — and Nick Broomfield’s haunting documentary “Marianne & Leonard: Words of Love,” which premiered on Sunday at the Sundance Film Festival, is a lovely illustration of the twists and turns of a complicated relationship that produced some of the gifted songwriter’s most indelible songs.

The Marianne of the title is Marianne Ihlen, a young Norwegian woman who Cohen met in the early ’60s on the Greek isle of Hydra, where artists of all stripes washed up to enjoy an idyllic life where, says one friend of Marianne’s, “there was so much freedom that people went too far with it.”

Leonard was a poet and novelist, Marianne a young mother with a rocky marriage. He thought she was the most beautiful woman he’d ever seen; she didn’t agree, but they fell in love and she became the muse who inspired songs like “So Long, Marianne” and “Bird on the Wire.”

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But those songs didn’t come until later, when the serious, melancholy poet had morphed into a singer-songwriter with a gift for mysterious, vividly evocative language. Even as Cohen became a star and she was widely known as his muse, their relationship had fractured and they lived apart more than together. In the documentary, singer Judy Collins remembers getting a letter in which Marianne wrote, “You recorded all his songs and I just want to tell you that you ruined my life.”

And yet the bond between Leonard and Marianne remained deep and abiding, and the two didn’t lose touch even when she moved back to Oslo, got a job as a secretary and got married. As Marianne lay dying in a Norwegian hospital, a friend sent word to Leonard, who wrote a moving letter in which he wrote, “Know that I am so close behind that if you stretch out your hand, I am think you can reach mine … Goodbye old friend. Endless love, see you down the road.”

She was read the letter while lying in her hospital bed, and softly said, “That’s beautiful.” At her request, a camera recorded her reaction, a scene in the film that brought much of the audience at the Marc Theatre to tears. (Three months after she died, so did Cohen.)

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Broomfield, whose past films include “Tales of the Grim Sleeper,” “Whitney: Can I Be Me” and “Kurt & Courtney,” introduced the film by calling it “my first love story.” But it is a love story that resists conventional structure, so “Marianne & Leonard” is elusive and elliptical, slipping back and forth in time even within a rough chronology.

As he does in many of his films, Broomfield inserts himself in this one. But that makes perfect sense: He himself went to Hydra as a 20-year-old photographer in 1968, where he befriended Marianne and briefly became one of her lovers. She also was instrumental in encouraging him to make his first documentary, which qualifies her as a muse to Broomfield (as well as others in the film, including singer-songwriter Julie Felix).

The abundant affection Broomfield feels for Marianne is evident in every frame of “Marianne & Leonard,” a love story between the two but also a love letter of sorts to the woman who gets first billing in the title.

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It’s a difficult film in many ways, with Broomfield forced to follow separate lives in which Leonard has ups and downs that end in glorious stardom, while Marianne simply fades from sight. But the memory of those years on Hydra hangs over the film, and the reverberations of a love that sent Cohen on his career trajectory.

As befits its subjects, “Marianne & Leonard” as much poetry as documentary — it’s a gentle, rhapsodic film, an emotional change of pace for its director and a moving portrait of a love that still resonates.