How does spatially white noise differ from diffuse noise
In a diffuse noise field the noise energy flows in all directions with equal probability. This does not mean that the noise at one point is uncorrelated with the noise measured at another point. On the other hand, for spatially white noise, also called incoherent noise, the noise signals at two different points in space are always uncorrelated.

An example for a diffuse noise field is noise in a car or in an office. An example for spatially white noise would be amplifier noise in a microphone array, where the noise in each channel is independent of the noise in other channels.