Sensitivity, like a superpower, can be a glorious and terrible gift. In Brett Morgen’s revelatory documentary “Kurt Cobain: A Montage of Heck,” which airs tonight on HBO, we see—almost from the inside—the evolution of Cobain’s sensitive brilliance and the art and destruction that it fed. Much of the film, which Morgen made with the full participation of Cobain's wife, Courtney Love, his daughter, Frances Bean Cobain, and his mother, father, and sister, consists of Cobain’s own creations: there’s the music, sounding glorious as ever, as well as art work, notebooks, films, and audio recordings that had never been made public. Morgen presents them in an artistic mashup of sound and image, interspersed with interviews with Cobain’s survivors. At the beginning, we see Super-8 footage of Kurt, a blond toddler waving and blowing kisses from his stroller; soon he’s wearing a sport coat and playing a tiny guitar. “I’m Kurt Cobain,” his little voice says proudly. The film ends just before his death, at twenty-seven. In between, “Montage of Heck” shows the evolution of an artist.

Cobain’s sensitivity is a focus throughout. His sister, Kimberly Cobain, says, “I’m so glad I never got that genius brain.” His mother, Wendy O’Connor, recalls that, as a little boy, Kurt “was so kind and so worried about people—if they were O.K., or if somebody got hurt.” The film takes us through Cobain’s childhood, in Aberdeen, Washington, showing that what began happily turned difficult when he became hyperactive, his sister was born, and his parents didn’t know how to handle him. They divorced when he was nine, which he found not just traumatic but humiliating. Humiliation is another focus.

In his teen years, Cobain became unruly and bounced from house to house, living with different relatives. His stepmother says that he always wanted to be the most beloved of the siblings and stepsiblings; he craved love and stability but continually found frustration and rejection. At one point, he was suicidal, but wanted to lose his virginity before dying; after a sad, somewhat cruel failed sexual encounter, he had a failed suicide attempt on a train track. At fifteen, he moved back home. Soon, he retreated to his room with a guitar. When Morgen asks Cobain’s sister if Kurt found the underground or the underground found him, she says, “I think they found each other. He was searching for whatever made him feel like he wasn’t alone and he wasn’t so different.”

Sound familiar? Cobain was once a teen-ager a bit like you were, looking for his people and his sound—an illustration by Cobain shows Lucy banging on Schroder’s piano and yelling, “I want punk rock, you blockhead!”—and finding himself when he did. His friend Buzz Osborne, of Melvins fame, made him some mixes: the Stooges, Flipper, Black Flag, the Vaselines, the Raincoats, the Slits, MDC, the Sex Pistols, Bad Brains. “I was completely blown away,” Cobain’s voice says. “I wore them out, played them every day. They expressed the way I felt socially and politically and it was the anger that I felt, the alienation.” He says, “This is what I’ve always wanted to do.” When he formed his band, and two people came to hear them play, they considered it a gig, and it was glorious. “Just the fact that we were playing music live in a room, it was the most incredible thing I’ve ever done,” Cobain said.

“Montage of Heck” makes Cobain’s written words and drawings move: writings in his ruled notebooks, lists of mixtape songs written in ballpoint pen, a drawing of a band called the Reaganites, ideas for names. (Boy in Heat, Drugs for Sale, Bliss, Erectum, Seringe, Man Bug, Godchild, Re-hash.) “Our final name is NIRVANA,” a page says. Watching “Montage of Heck” feels like being a teen-ager in the eighties or nineties: making mixtapes, making weird collages, scrawling dreams in a spiral notebook, going to shows where bands play in front of projections of, say, slaughterhouse footage. When paired with Cobain’s music, the effect can be thrilling, and a poignant reflection on time.

As the story progresses, we learn that Cobain, who soon starts dating the supportive Tracy Marander, has chronic stomach pain. He throws up a lot, has terrible, violent dreams. The Nirvana bassist Krist Novoselic mentions a bad review and says that Cobain hated being humiliated. After a while, to cope with pain of all kinds, Cobain starts secretly doing heroin. Meanwhile, he’s writing, practicing, making lists of how to proceed and where to send his demos. “Sub Pop,” a notebook page says. That was the mighty album “Bleach.” Their fan base and esteem grew.

When Cobain played his mother the master tape of “Nevermind” for the first time, she says, she felt “scared.” She knew that it would change everything, and she almost started crying, not from pride but from worry. “I said, ‘You better buckle up. Because you are not ready for this,’ ” she says.

She was right. It changed everything for millions of us, and consequently for the band. Whether or not you already knew and loved “Bleach,” Nirvana’s first album, “Nevermind” was a revelation—powerful, fun, enraged, delicate, brilliant. (It was also funny. One of the few details I wish Morgen had illuminated more is Cobain’s sense of humor.) Hearing “Nevermind” felt like a physically transformative experience; watching the video for “Smells Like Teen Spirit” did, too. For some kids, seeing those thrashing teens and anarchist cheerleaders in the gym was like seeing themselves on TV; for others, it was like seeing the future. Morgen manages to make that video, that song, less familiar, by slowing the footage down and pairing it with an angelic cover version.

Novoselic, now, says that it was “kind of traumatic” to go “from complete obscurity to being the No. 1 band in the world.” He says that he withdrew a bit, and drank. He says, “I’m lucky I had beer and wine. Kurt had heroin.”

Fame, like love, is seeing, recognition, fuelled by connection. Being seen, for a very sensitive person, can be terrifying. In interviews from the nineties, Novoselic and the drummer Dave Grohl, if a bit dorky, seem comfortable, even gregarious; Cobain looks like he wants to disappear. In an MTV clip, a v.j. asks them if the energy at their shows has changed. Novoselic chuckles and tries to explain it; Cobain, next to him in sunglasses and a puffy daffodil-yellow high-collared gown, says, “Everyone wants to be hip. Everyone wants to be accepted.” He looks like he’s channelling seventies Eno or Bowie, and hoping to float up to space. In another clip, Grohl and Novoselic gamely try to answer a question about music and success, and Kurt slumps onto the table.

When Cobain married Courtney Love, a rock star in her own right with a personality to match, the attention only grew. An article in Vanity Fair by Lynn Hirschberg asked if they were “the grunge John and Yoko” or “the next Sid and Nancy” and said, “sources maintain that the Cobains have been heavily into heroin,” quoting a friend who said that Love was pregnant and shooting up. Cobain flipped out, writing angry letters (“may the riot grrls hunt you down”), feeling enraged and humiliated. He said later, “I feel like people want me to die, because it would be the classic rock and roll story.” At a giant outdoor stadium, Cobain says to a jillion fans, “We’ve had some pretty extreme things written about us. Especially my wife, and she thinks everybody hates her now. So why don’t you give her a message and say, Courtney, we love you.” He counts to three and the whole stadium shouts, “COURTNEY, WE LOVE YOU!” He smiles, says thanks, looks gently happy, and then launches into the fantastic “Territorial Pissings.” It’s a heartbreaking and beautiful moment, and you sympathize with the whole mess of it.