Ultracold molecules represent a fascinating research frontier in physics and chemistry, but it has proven challenging to prepare dense samples at low velocities. Here, we present a solution to this goal by means of a nonconventional approach dubbed cryofuge. It uses centrifugal force to bring cryogenically cooled molecules to kinetic energies below 1 K x k(B) in the laboratory frame, where kB is the Boltzmann constant, with corresponding fluxes exceeding 1010 per second at velocities below 20 meters per second. By attaining densities higher than 10(9) per cubic centimeter and interaction times longer than 25 milliseconds in samples of fluoromethane as well as deuterated ammonia, we observed cold dipolar collisions between molecules and determined their collision cross sections.