Forty-year-old grunge figurehead Billy Corgan no longer has to hide his inner progressive rocker. In the years since the break-up of his seminal 1990s alternative band Smashing Pumpkins, he has flirted listlessly with pop-rock in the short-lived band Zwan and noodled aimlessly on a quasi-electronic 2005 solo album. In the process, he abandoned what earned Smashing Pumpkins its devout fan base on 1993’s “Siamese Dream,” namely huge distorted guitar hooks, lushly orchestral production, and a vaguely misanthropic worldview.

For the Pumpkins’ “comeback” album, “Zeitgeist,” the band’s first since 2000’s “MACHINA/ The Machines of God,” Mr. Corgan not only digs back into those hallmarks, but adds the patina of a conceptual thematic framework, some self-important cover art, and includes a nine-and-a-half-minute musical expedition titled “United States.”

Of all the iconic 1990s grunge bands, Smashing Pumpkins was most influenced by 1970s-era progressive rock and gothic rock, and on “Zeitgeist,” the prog-rock elements that always lurked just beneath the surface of its records finally comes to the fore, making it the band’s heaviest album to date. But that ferocity comes at the cost of Mr. Corgan’s talent for writing instantly catchy, mid-tempo, glammed-up goth-pop. The Pumpkins were also the most mainstream alternative band hatched in the ’90s, deemed “alternative” more by the company of its peers — Hole, Nirvana, Liz Phair, Pearl Jam — than by the music they made. But with “Zeitgeist,” Mr. Corgan ignores the crass pop sensibility that made the Pumpkins such a radio and arena staple in the first place, leaving a slightly more melodic Tool album in its wake.

“Zeitgiest” is a Smashing Pumpkins album pretty much in name only. The group disbanded in 2000 after “MACHINA.” For this reformation, only original drummer Jimmy Chamberlin returns to Mr. Corgan’s fold, with original guitarist James Iha and bassist D’Arcy Wretzky replaced by Jeff Schroeder and Ginger Reyes, respectively, for the touring version of the band. Mr. Corgan was always the Pumpkins’ focal point and chief songwriter, but he did share song-writing credits with Mr. Iha on some songs through the years, and one has to wonder what impact the departed members had in shaping the band’s peak material. Working only with Mr. Chamberlin — who also played with Zwan and on Mr. Corgan’s solo album — and producers Roy Thomas Baker (Queen, the Cars) and Terry Date (Pantera, Deftones), “Zeitgeist” might as well be a Billy Corgan solo release.

And this time out he’s not trying something wholly new, as he did with his 2005 solo album, “The Future Embrace.” From the lead track — the full-throttle “Doomsday Clock” — on through the epic “United States,” the new album finds Mr. Corgan in a rambunctious mood.

“Doomsday Clock” kicks off with a flurry of drums and howling guitar, sounding like an opening salvo from a Mars Volta album. Lead single “Tarantula” sprints along, powered by Mr. Chamberlin’s huge hitting and a laser-like guitar thrust. Peppery guitar solos and screaming fretwork strafe through parts of all the songs. And come “United States,” Mr. Corgan has turned his Pumpkins into a full-fledged prog outfit, building the track around a slow boil of tribal percussions and guitar textures that unfurls into something as varied and rocking as early 1970s Genesis.

Lyrically, though, Mr. Corgan isn’t on a prog science-fiction/fantasy bender. Introspective angst has always been his song-writing bedfellow, and on “Zeitgeist” he tries to make that disaffection feel relevant. From the title down to the album cover — a solitary image of the Statue of Liberty up to her knees in a rising sea by politically minded graphic designer Shepard Fairey — everything about “Zeitgeist” makes a half-hearted bid to talk about something going on now. The cover may bring global warming to mind, or may be a comment on the consequences of war, but neither is treated explicitly.

Instead, Mr. Corgan plies his usual navel-gazing loneliness (“Doomsday Clock”), romantic let downs (“7 Shades of Black,” “Bleeding the Orchid,” “That’s the Way [My Love Is]”) adds some nonspecific alienation (“United States”), and vaguely topical blushes with a quasi-patriotism (“For God and Country”). By the time faint traces of Mr. Corgan’s softer pop touch appears in the album’s latter half, the damage has already been done. The synth-pop “Pomp and Circumstance” and especially the jaunty, easygoing “Neverlost,” offer the sort of throwaway pleasures on which Smashing Pumpkins built its traditional rock-star career. But tucked away after all the loud, brash tantrums, these few moments of catchy pop can’t compensate for the album’s substance-less screams for attention.