Intensity correlations and noise reduction are observed and characterized in the broadband supercontinuum generated by spatio-temporal solitons propagating in air, i.e., in filamentation of ultrashort laser pulses. Large correlations and reduction of the laser noise are observed already at the first steps of the filamentation process, while further propagation results in cascaded χ(3) broadening processes and yield complex correlation maps. The spectral range yielding an optimal laser noise reduction of 3.6 dB is found to cover 10 nm around the fundamental wavelength.