Diffusing sequences keep their scattering properties because scaling for wavelength preserves their Fourier transform.

Evidence

The second desirable property of these sequences is that the Fourier transform is unaffected if the wavelength of the incident sound varies. This has the effect of changing the scale of the sequence, but again one can show that the resulting sequence still has the same properties as the original sequence. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2088