  We study a strongly interacting crowded system of self-propelled stiff
filaments by event-driven Brownian dynamics simulations and an analytical
theory to elucidate the intricate interplay of crowding and self-propulsion. We
find a remarkable increase of the effective diffusivity upon increasing the
filament number density by more than one order of magnitude. This
counter-intuitive 'crowded is faster' behavior can be rationalized by extending
the concept of a confining tube pioneered by Doi and Edwards for highly
entangled crowded, passive to active systems. We predict a scaling theory for
the effective diffusivity as a function of the P\'eclet number and the filament
number density. Subsequently, we show that an exact expression derived for a
single self-propelled filament with motility parameters as input can predict
the non-trivial spatiotemporal dynamics over the entire range of length and
time scales. In particular, our theory captures short-time diffusion, directed
swimming motion at intermediate times, and the transition to complete
orientational relaxation at long times.
