We demonstrate a 0.56-GW, 1-kHz, 4.2-ps, 2.74-mJ deep-ultraviolet (DUV) laser at ∼257.7  nm with a beam propagation factor (M^2) of ∼2.54 from a frequency-quadrupled cryogenic multi-stage Yb-doped chirped-pulse amplifier. The frequency quadrupling is achieved using LiB_3O_5 and β-BaB_2O_4 crystals for near-infrared (NIR)-to-green and green-to-DUV conversion, respectively. An overall NIR-to-DUV efficiency of ∼10% has been achieved, which is currently limited by the thermal-induced phase mismatching and the DUV-induced degradation of transmittance. To the best of our knowledge, this is the highest peak-power picosecond DUV source from a diode-pumped solid-state laser operating at kHz repetition rates.