  We study two numerical approximations of solutions of nonlocal diffusion
evolution problems which are inspired in algorithms for computing the bilateral
denoising filtering of an image, and which are based on functional
rearrangements and on the Fourier transform. Apart from the usual time-space
discretization, these algorithms also use the discretization of the range of
the solution (quantization). We show that the discrete approximations converge
to the continuous solution in suitable functional spaces, and provide error
estimates. Finally, we present some numerical experiments illustrating the
performance of the algorithms, specially focusing in the execution time.
