We report what we believe to be record performance for a high average power Yb:YAG cryogenic laser system with sustained output power. In a CW oscillator-single-pass amplifier configuration, 963 W of output power was measured. In a second configuration, a two amplifier Yb:YAG cryogenic system was driven with a fiber laser picosecond ultrafast oscillator at a 50 MHz repetition rate, double-passed through the first amplifier and single-passed through the second, resulting in 758 W of average power output. Pulses exiting the system have a FWHM pulsewidth of 12.4 ps, an energy/pulse of 15.2 μJ, and a peak power of 1.23 MW. Both systems are force convection-cooled with liquid nitrogen and have been demonstrated to run reliably over long time periods.