If rock history has taught us anything, it’s that any band that has split up can and inevitably will reform, no matter how acrimonious their “musical differences”. American punk-rock group At the Drive-In proved as much in 2012, when the group reunited for a spate of shows (including a headlining appearance at Coachella) 11 years after their abrupt and messy dissolution. Now, after a second run of concerts last spring, the group have announced their first new music for 17 years, in the form of their fourth full-length album, In.Ter A.Li.A.

Rock seemed in something of a lull when At the Drive-In delivered their breakthrough third album, Relationship of Command, in 2000, the album’s razor-edged, propulsive and cerebral punk-rock a blessed respite from the then-ascendant likes of Limp Bizkit, et al. The group had formed seven years earlier in their hometown of El Paso, Texas, and from the start their chemistry was tempestuous. Their membership was in flux throughout their first three years, with singer Cedric Bixler-Zavala and guitarist Jim Ward the only constants until their 1996 debut album, Acrobatic Tenement. It was here that At the Drive-In’s classic lineup took shape, with the arrival of rhythm section Tony Hajjar (drums) and Paul Hinojos, and Cedric’s best friend Omar Rodríguez-López, a mercurial lead guitarist with a headful of avant-garde ideas.

In the years that followed, the group perfected a bombastic, sinewy post-hardcore sound, drawing influence from underground iconoclasts Fugazi, along with a slew of more unexpected inspirations. The tension between their penchant for punk anthemicism, their rhythmic complexity and restless invention electrified Relationship of Command. Helmed by visionary producer Ross Robinson (responsible for the maligned Limp Bizkit, but also for Slipknot, and the gory, brilliant Burn, Piano Island, Burn by the Blood Brothers), released on the Beastie Boys’ endlessly hip Grand Royal imprint, and boasting a guest appearance from king of punk Iggy Pop himself, it threatened to make actual, proper rock stars of At the Drive-In.

But almost instantly, the group began to disintegrate. The differences between the two camps – the rail-thin, afroed Cedric and Omar on one side, their bandmates on the other – were partly musical. “We’d get ridiculed for playing Pink Floyd, Tom Waits, dub music and Talk Talk on the tour van stereo,” Cedric told me in 2004. When the group formed, Cedric said he’d been drawn to Jim Ward because, unlike most musicians in El Paso, “he seemed committed to working, to achieving something.” Now, however, Omar and Cedric felt held back by Ward’s groundedness. Also, Cedric and Omar had embarked on a journey of chemical misadventure, heroin, crack cocaine and psychedelics fuelling ambitions to junk their punk-rock blueprint, and estranging them from their Drive-In kin.

At the Drive-In perform at Roskilde festival, Denmark, in 2016. Photograph: Andrew Benge/Redferns

Early in 2001, mainstream success within arm’s reach, the group announced a hiatus that soon became indefinite. Later that year Ward, Hinojos and Hajjar formed sturdy emo-rock outfit Sparta, while Omar and Cedric moved to a house in Long Beach, California named Anikulapo (after their hero Fela Kuti), took terrifying amounts of drugs and conceived their new vehicle, the Mars Volta, exploring an indefinably proggy, dubby, jazzy, Latin-inspired sound over a series of fearless, complex, successful concept albums. “Compromise,” Cedric explained, “is no way to live.”

Still, despite the success of the Mars Volta and Sparta, the thwarted promise of At the Drive-In continued to haunt its former members. They reunited in 2012, following years of big money offers to reform, having mended their friendship a while earlier. But the reunion tour was marred by accusations that they were cashing in on nostalgia, and that Rodríguez-López’s performances were lacklustre, compared with his earlier acrobatic stageplay (Omar later explained that his mother’s death, a week before the tour began, had left him depressed and disaffected). Their 2016 jaunt was much better received, but was undertaken without Jim Ward, who was replaced by his Sparta bandmate Keeley Davis. Ward’s exit remains shrouded in mystery, Cedric telling NME only that “we were super-ready to do this, and he wasn’t”.

Without Ward, however, the group have finally recorded that long-awaited fourth album, to be released on 5 May. “It was about getting back to that primordial self,” says Cedric, explaining how they found the thread of ATDI’s sound after 17 years of silence. “We essentially agreed, ‘We need to honour the last record. We need to go forward, be the fucking core of what we are, and ignore everything we learned in our years apart.’”

Though only two tracks have yet been made public, In.Ter A.Li.A sounds exactly like you’d imagine the follow-up to Relationship of Command would have sounded, had At the Drive-In’s members not gone off on their vision quests back in 2001. And it’s to the group’s endless credit that, 17 years on, their hot-footed, breath-stealing, high-wire punk rock still somehow sounds like the future.