We have demonstrated an 18.9 nm Ni-like molybdenum soft x-ray laser, pumped by a compact all-diode-pumped Yb:YAG laser. The solid-state pump laser produces 8.5 ps pulses with up to 1 J energy at 10 Hz repetition rate. This diode-pumped laser has the potential to greatly increase the repetition rate and the average power of soft x-ray lasers on a significantly smaller footprint.