We study and demonstrate the efficient parametric amplification of spectrally incoherent broadband nanosecond pulses to high energies. Signals composed of mutually incoherent monochromatic lines or amplified spontaneous emission are amplified in a sequence of optical parametric amplifiers pumped at 526.5 nm, with the last amplifier set in a collinear geometry. This configuration results in 70% conversion efficiency from the pump to the combined signal and idler, with a combined energy reaching 400 mJ and an optical spectrum extending over 60 nm around 1053 nm. The spatial, spectral, and temporal properties of the amplified waves are investigated. The demonstrated high conversion efficiency, spectral incoherence, and large bandwidth open the way to a new generation of high-energy, solid-state laser drivers that mitigate laser-plasma instabilities and laser-beam imprint via enhanced spectral bandwidth.