The three-decade run of the Beastie Boys came to an abrupt halt in 2012, when Adam Yauch, a member of the trailblazing rap trio known as MCA, died of cancer at age 47.

In the aftermath, Michael Diamond, a.k.a. Mike D, one of two surviving Beasties, set out to make music on his own. Again and again, he queued up recording software on his computer and tried to create. Again and again, he couldn’t go through with it.

“The amount of grieving and sadness that I would feel,” Diamond recalled in an interview in May, “the easiest way to not feel that was to shut the computer down and walk away from it. It was too much for me to process to stay focused and creative.”

After dipping into production for others, and with help from family, Diamond, 60, has returned to music making. On Aug. 28, he will release a solo album, “Thank You,” the first new music by a member of the Beastie Boys since Yauch’s death 14 years ago.

“Thank You” was made with the close involvement of Diamond’s sons, Davis and Skyler: Brooklyn-born Californians, now in their early 20s, who have their own group, Very Nice Person, and honed their production skills on the vintage audio equipment they pilfered from their dad’s home studio in Malibu, Calif.

From its first notes, “Thank You,” credited to Mike D 5D, is a searing, lo-fi blast of analog synthesizer noise and smashed industrial beats, bearing the influence of dub and the dystopian New York punk band Suicide. At recent club gigs announcing the project, Diamond and his five-member band, including Davis and Skyler, leaped up and down in Mike D 5D-branded jumpsuits, like a multigenerational punk-aerobics class.

With a level of introspection rarely heard on Beastie Boys albums, “Thank You” also paints a therapeutic portrait of Diamond adjusting to life as a sexagenarian rapper emeritus, wrestling with the responsibilities of parenthood and the sense of being “far away and out of touch,” while also searching for a way to stay in the game. “I need a Plan B / retired M.C.,” Diamond yelps on one of the album’s most boisterous tracks, “What We Got.”

“It’s musically immature, but lyrically more mature,” Diamond, graying and still rail-thin, summed up in the fire-warmed lounge of a Lower East Side hotel, a few hours after he finished spinning records for an online radio show in Brooklyn.

Diamond grew up on the Upper West Side of Manhattan, the son of art-world insiders, and from a young age felt destined for a creative life. A formative experience happened at age 17 on a trip to the Brooklyn Academy of Music to see Laurie Anderson’s landmark performance-art piece “United States.”

“She had a tape-head on her violin and tape on her bow, and there’s a video projection,” Diamond recalled, his eyes widening with the memory. “It was really the first multimedia thing I saw. I was completely exhilarated. I was like, ‘That’s what I’m gonna do.’”

By that time, the Beastie Boys were morphing from their punk-rock origins into rap, and settling into a three-piece lineup of Yauch, Diamond and Adam Horovitz, a.k.a. Ad-Rock. The story of their rise is like a raunchy 1980s New York version of a fairy tale.

Coming under the wings of Rick Rubin and Russell Simmons at Def Jam Recordings, they toured with Madonna and their 1986 debut, “Licensed to Ill,” bumped Bon Jovi from the top of the Billboard 200 chart to become the first rap album to reach No. 1. In testosterone-drenched anthems like “(You Gotta) Fight for Your Right (To Party!)” and “Girls,” they fully embraced their personae as obnoxious, smirking party boys — though they came to loathe it.

Successive reinventions on albums like “Paul’s Boutique” (1989), “Check Your Head” (1992) and “Ill Communication” (1994) made them prime zeitgeist movers of the ’90s, their three-part comic rhymes densely layered with references drawn from pop-culture’s dustbin. Diamond’s thin voice put him in a middle zone between Yauch’s hoarse gruff and Horovitz’s sharp nasal tone.

“These guys were intrepid creators,” said Dan Charnas, an associate professor at the Clive Davis Institute of Recorded Music at New York University. “By the ’90s their work, musically and aesthetically, anticipated how pop culture would shift over the next 10 years: hip-hop merging with punk and alternative, street culture with skater culture, satire with social good.”

Yauch became the group’s conscience, cofounding the Tibetan Freedom Concerts and, on the 1994 track “Sure Shot,” atoning for the band’s past misogyny: “To all the mothers and the sisters and the wives and friends / I want to offer my love and respect to the end.”

Yauch’s death brought an end to the musical partnership that Diamond and Horovitz had been part of since they were teenagers.

“There was a very recognizable thing that happened between our three voices,” Diamond said. “It was a magical thing, a rare gift that the three of us all got to share together. But that doesn’t exist anymore. So it took a minute to just get comfortable with it.”

Diamond largely stepped back from music to care for his sons, who were then preteens. He and Horovitz also tended the Beasties legacy through a book and a documentary. But both men’s musical productivity plunged. In an interview, Horovitz said that for years he has maintained a near-daily routine of making music on his laptop, but hasn’t released any of it.

When asked why not, Horovitz mumbled: “Good question.”

Diamond produced for others, working on the most recent album by the high-concept Swedish punk band the Hives (“The Hives Forever Forever the Hives,” released last year). But he had a revelation: “I shouldn’t be projecting my ideas onto any other artist. I should be saving that for myself.”

So Diamond began sitting in on sessions with his sons, who mingle with some of the top producers in Los Angeles. In conversation, Davis, 23, and Skyler, 22, finish each other’s sentences with surfer-voice uptalk and call their father Mikey. (They are also only loosely familiar with the Beastie Boys songbook, having to bone up on tracks for their recent club tour.)

Skyler: “Mikey’s had a funny trajectory of his vibes. Our more recent memory is his retired lifestyle.”

Davis: “He was, like, fulfilled in other ways. And then it got to a certain point where he started getting on the mic more and just messing around in jams and stuff. And then one day he went to France and came back and was like, ‘This is happening now.’”

The Diamonds began creating songs with a cast of musicians and producers, including Carter Lang, who has worked with SZA and Justin Bieber; and Tyran Donaldson, another SZA collaborator. They held long, anything-goes sessions, unencumbered by deadlines or pressure to generate hits — an artist-led process that Lang likened to his experience with Bieber’s recent “Swag” albums.

“They’ve been able to create this freeing feeling,” Lang said. “This environment where when I enter it, the industry grind just falls away and you’re able to create out of pure discovery and love and curiosity.”

The studio was packed with a menagerie of ancient gear that the musicians tinkered with like lost toys; songs like “That’s Right” throb with noisy feedback and prickly, distorted rhythms. Horovitz lent Skyler and Davis a 1980s-vintage sampler that came with floppy disks still holding Beastie Boys beats. “It’s a time machine,” Donaldson recalled with a chuckle. “They’d be trying to find a sound, and you’d randomly hear a drum break that was on a Beastie Boys song.”

The result is a blending of the murkily tuneful sound of Very Nice Person with a more aggressive rhythmic punch that derives from the lo-fi punk of Diamond’s youth.

I suggested to Diamond that the process with his two sons sounded not dissimilar to how the Beastie Boys would hole up at a studio playground for months before they emerged with a breakthrough sound.

“It gets weirder than that,” Diamond said. “I grew up the youngest of three brothers. In the band, I was the middle of three brothers, in a sense. And then I end up having two boys. There you go.”

Diamond’s sons, he said, could critique his vocals with a candor that none of the other producers — all decades younger than Diamond — could summon.

“Out of anybody I worked with, they were more innately comfortable with pushing me on my vocals,” Diamond said. “Their big line was, ‘That was good, but you can top it.’

“So they didn’t totally annihilate me,” he added in dad-joke deadpan.

“I don’t know that Mike would have done this on his own,” Horovitz said. “We spent the bulk of our lifetime being in a band, a threesome that did everything together. And doing something on your own feels weird.” He added, “I think it’s great that Mike has recorded a record, especially with his kids. I think it is probably really helpful and healing to him.”

Diamond sounds invigorated on “Thank You,” but also deeply reflective, with lyrics that seem to address the stresses of parenthood and a broken relationship — Diamond is separated from Davis and Skyler’s mother, the filmmaker Tamra Davis — as well as his own search for purpose. “We all come from trauma / We fill our worlds with drama,” he raps on “Make It Stop.” On “I Don’t Care,” he says, “I try to please everyone / It’s killing me.”

Elsewhere, music serves as a metaphor for how to refresh one’s life. “Switch up connection / Switch up direction,” he raps on “Switch Up,” driven by a very ’90s-style accelerated drum ’n’ bass rhythm track.

“I think this record very much reflects this time of my life,” Diamond said, “of my kids being their own entities in the world and collaborating with me.”

“It’s really about being honest,” he added. “The things that I’m grappling with at a different age in life that weren’t present for me when I was in the band.” He added, “I think it’s my process of being able to be OK with the unknown a bit.” Over about two hours of conversation, he mentioned therapy five times.

His sons said they were worried their father’s comfortable lifestyle would yield a “luxury rap vibe,” with lyrics about being “an older white rapper talking about drinking wine,” as Skyler put it. Instead, Diamond came to sessions with notebooks filled with deep psychological reflections he had collected on silent retreats.

“It’s like the whole record’s therapy rap,” Davis said. “It’s really deep therapy concepts. We were just like, ‘That’s a sick vibe.’”

Skyler added: “That’s just where Mikey’s at.”