Sharmeen Obaid-Chinoy and Trish Dalton’s documentary, streaming on Hulu from June 25, presents a largely first-person portrait of the woman behind the wrap dress.

The engaging Diane von Furstenberg: Woman in Charge begins with a clip from David Letterman’s late-night show, where he introduces the designer with, “Welcome the woman who reinvented the dress.” He laughs and says, “Really? Reinvented the dress?” But that big claim isn’t entirely wrong. In the 1970s, von Furstenberg’s wrap dress was more than a trendsetter. Like the person who emerges in this largely first-person documentary, the dress became emblematic of a professional but sexy independent woman.

Much of what von Furstenberg says here she has said before, in interviews or in her two memoirs, notably The Woman I Wanted to Be (2014). But in retelling her story on screen, she has an inviting style full of the confidence and self-possession that is at the heart of her brand and that defines the documentary’s style. The film presents its subject in glittering terms, but it is also constantly fascinating, and gracefully directed in an unflashy manner by Sharmeen Obaid-Chinoy and Trish Dalton. (Obaid-Chinoy has won two Oscars for shorts and is set to direct Daisy Ridley in Star Wars: New Jedi Order.)

In her early 20s she married the rich playboy Prince Egon von Furstenberg and recalls the chilly reception his aristocratic German family gave his middle-class Jewish bride. In a line that captures her wry tone, she says, “When I went to the Furstenberg castle, I thought ‘Maybe they will poison me.’”

She was also beginning to design, creating wrap tops inspired by those that ballerinas wear to rehearse, but in bright jersey prints. In her account, fashion was merely a means of gaining independence, not a passion. She moved to New York, where her business flourished, and she and the endlessly philandering bisexual prince became the It couple of the moment. But she was soon over being part of a couple. “Divorce for me was freedom,” she recalls.

On her own, she hit Studio 54, and looking back acknowledges her free and easy sex life, in sync with the times but more glamorous than most. “I was with Warren Beatty and Ryan O’Neal on the same weekend,” she says. One friend says that von Furstenberg has always been unapologetic about her sexuality, but her own comments suggest something bolder: that she didn’t think there was anything to apologize for in the first place. “I was having a man’s life in a woman’s body,” she says, echoing an often-quoted remark of her own.

The wrap dress was also affordable, which gave von Furstenberg reach and made her a plausible role model. Her family is more revealing than her celebrity friends. Her daughter recalls a childhood left largely in the care of Diane’s mother, saying, “I don’t know if you want to use the word neglected or free.” Von Furstenberg admits that as a very young mother she probably didn’t have enough time for her two children, but that they were always in her heart.  

More colorfully, she recalls turning down a proposed three-way with Mick Jagger and David Bowie. She considered it, she says, thinking “Well this is something I can tell my grandchildren about.” Obviously she told them anyway. The next thing we hear — in a juxtaposition that suggests the film’s smooth construction — is her grown granddaughter saying that turning those two down at the height of their fame was a “really epic” move.

Barry Diller, the chairman of IAC, to whom von Furstenberg has been married since 2001, speaks about their relationship, which goes back to the ’70s when he was head of Paramount Pictures. He recalls the freedom of that era, when everyone slept with everyone in any combination. They were nonexclusive lovers for several years, were apart, then together again.