Cross-correlation of fully diffuse wavefields averaged over time should converge to the Green’s function; however, the ambient seismic field in the real Earth is not fully diffuse, which interferes with that convergence. We apply blind signal separation to reduce the effect of spurious non-diffuse components on the cross-correlation tensor of the ambient seismic field. We describe the diffuse component as having uncorrelated neighboring frequencies and equal intensity at all azimuths, and an independent (i.e., statistically uncorrelated) non-diffuse component arising from a spatially isolated point source for which neighboring frequencies are correlated. Under the assumption of linear independence of the spurious non-diffuse wave outside the stationary phase zone and the constructive interference of noise waves within that zone, we can suppress the spurious non-diffuse component from the noise interferometry. Our numerical simulations show good separation of one spurious non-diffuse noise source component for either non-diffuse Rayleigh or Love waves. We apply this separation to the Rayleigh-wave component of the Green’s function for 136 cross-correlation pairs from 17 stations in Southern California. We perform beamforming over different frequency bands for the cross-correlations before and after the separation, and find that the reconstructed Rayleigh waves are more coherent. We also estimate the bias in Rayleigh wave phase velocity for each receiver pair due to the spurious non-diffuse contribution.