We theoretically and experimentally study the nonlinear propagation of polychromatic light in curved waveguide arrays. We show that at moderate light powers the nonlinear self-action breaks the left-right symmetry of the polychromatic beam, resulting in the separation of different spectral components owing to the wavelength-dependent spatial shift. At high light powers a diffraction-managed polychromatic soliton is formed. These results demonstrate new possibilities for tunable demultiplexing and spatial filtering of supercontinuum light.