To add to Duke’s very informed post above, Danny Richie’s GR Research OB subs are the "fastest" I’ve ever heard. Danny chose paper as the cone material for the drivers he designed for his subs for a few reasons: He finds paper to provide greater resolution than aluminum at small signal levels, the result of paper’s lower mass and energy storage in comparison to aluminum; he finds paper to provide more natural timbre than aluminum; and paper-coned woofers can be used to a higher x/o frequency, his OB sub being usable up to 300Hz. Danny offers the same woofer with an aluminum cone (marketed through Rythmik Audio), but recommends the paper version for highest sound quality.
The "fast" characteristic of a sub is not, as Duke just said, the result of it starting quickly (bass frequencies are relatively slow), but rather of it stopping quickly (the OB sub has been described as "stopping on a dime"). That results in the sub not filling in the spaces between musical material with noise, from both the cone itself as well as the sub cabinet---self-induced resonance. The OB nature of the sub also lessens the room’s ability to add it’s own noise---the "boom" subs are notorious for creating. An OB sub doesn’t "load" the room the way sealed and ported subs do, exciting fewer room modes.
Danny was already offering OB subs when he learned of fellow-Texas resident Brian Ding of Rythmik, who had developed and patented a new servo-feedback woofer design. Danny proposed they work together at designing a woofer optimized for Open Baffle use and employing Brian’s servo-feedback circuitry. The resulting sub is very special---the world’s only Open Baffle-Dipole/Servo-Feedback sub! Brian himself offers an extensive line of aluminum-coned Servo-Feedback subs through Rythmik Audio, in 8", dual 8", 12", dual 12", 15", dual 15", and soon-to-be-available 18", some of them in sealed models only, some in ported only, and some in both. Very "fast" sounding subs is what Rythmik Audio is known for (Sterling Sound in NYC, famous for their superior-sounding mastering, has six of the sealed 15" in their monitor systems), and GR Research has a few DIY sub models (sealed in addition to the afore-mentioned OB), as well as loudspeakers. There is no longer any reason or need to settle for "slow", bloated, boomy subs!