Recent results in the development of diode-driven high energy, high repetition rate, picosecond lasers, including the demonstration of a cryogenic Yb:YAG active mirror amplifier that produces 1.5 J pulses at 500 Hz repetition rate (0.75 kW average power) are reviewed. These pulses are compressed resulting in the generation of ${\sim}5~\text{ps}$ duration, 1 J pulses with 0.5 kW average power. A full characterization of this high power cryogenic amplifier, including at-wavelength interferometry of the active region under ${>}1~\text{kW}$ average power pump conditions, is presented. An initial demonstration of operation at 1 kW average power (1 J, 1 kHz) is reported.