Pneumatic launchers use the mass of a compressed air source (the chamber) to accelerate a projectile in the barrel. Pneumatic launchers are the simplest in theory, but often getting them to work efficiently is slightly more complicated than combustions.
A pneumatic launcher, in my opinion, completely relies on the valve for any type of performance. Valves range from a simple ball valve (slowest) to piston and spool valves (faster) to burst disks (fastest). Sometimes, the projectile itself is the valve. My point is, there are many variants of pneumatic cannons, and often, thinking outside the box can yield better results than with combustion launchers.