A class of models of stochastic processes and fields with a convex correlation function and a given one-dimensional distribution is constructed on the basis of stationary point flows. It is sometimes possible to improve successively the multi-dimensional distributions by using the summability of the realizations, the convergence being weak for non-negative processes. The convergence of approximate models of Gaussian fields, obtained by special randomization of the spectral resolution, is studied. The models can be realized quite easily on a computer.