New York filmmaker S.A. Crary’s documentary “Kill Your Idols” ambitiously tries to connect the anti-traditional No Wave bands of New York in the late 1970s and early 1980s to the 2002 explosion of fashionably marketable New York and Brooklyn post-punk inspired rock. But while Mr. Crary’s sincere appreciation for the music and personalities of both eras is plainly evident, he writes checks his movie just can’t cash.

“Idols” locates No Wave’s ground zero in the 1972 formation of Suicide, the synth duo of Martin Rev and Alan Vega. Mr. Crary positions the group as the antithesis of escapist cool bands such as the New York Dolls. In an interview, Mr. Rev said that Suicide couldn’t afford to dress up and that escape wasn’t in the band’s nature. Archival footage shows the sunglasses-wearing Vega and Rev eking out their throbbing, buzzing music in some shadowy, grainy place that looks and feels both cool and dangerous.

As “Idols” fast forwards to 1977 and introduces downtown habitué Lydia Lunch, who formed Teenage Jesus and the Jerks, Mr. Crary allows No Wave’s creators — Ms. Lunch, her Teenage Jesus band mate Jim Sclavunos, DNA’s Arto Lindsay, Theoretical Girls’ Glenn Branca — to reminisce about the hows and whys of their non-aesthetic. Two common threads emerge: the singularity of their sound and a non-careerist impulse to “disregard the influences that made me want to do music in the first place,” according to Ms. Lunch.

More philosophical than aesthetic, this impulse inspired the next generation of bands Mr. Crary interviews — Swans’ Michael Gira, Sonic Youth’s Lee Ranaldo and Thurston Moore, Foetus’s Jim Thirlwell. But when “Idols” leapfrogs to 2002’s up-and-coming New York noisemakers — the Yeah Yeah Yeahs, Liars, Black Dice, A.R.E. Weapons, Gogol Bordello, Flux Information Sciences — these young artists look like the myopic inverse of the scene that Mr. Crary says influenced them.

Karen O and Nick Zimmer of the Yeah Yeah Yeah’s, for instance, even admit that they had a name and a grassroots marketing campaign mapped out before they had come up with any songs; the insipid self-importance of A.R.E. Weapons’ vocalist, Brian McPeck, couldn’t be more incompatible with Ms. Lunch’s confrontational spirit.

Credited as the film’s producer, director, cameraman, and editor, Mr. Crary refreshingly gives “Idols” a loose, low-tech vibe that compliments all the profiled artists’ scrappy ethos. And the roughness of the archival No Wave footage — so distressed and muddy it sometimes looks as if it were found on the street and passed through an airport x-ray machine before being developed — heightens this shadowy mood. But as the always razor-sharp Ms. Lunch observes, when a scene “adopts nostalgia as the basis for something you’re going to create from, that, for me, indicates an intellectual bankruptcy” — a condition that ultimately infects the entirety of “Kill Your Idols.”