Correlated x y displacement in image

I want to add a time dependent noise to image, which amounts to adding a pixel dependent noise. For this I used "B = imwarp(A,D)" method to accomplish this, where A is an image of size (rows,cols) and the displacement field D is a matrix (rows,cols,2). The problem I am having is that when I have correlated x and y displacement fields, i.e., (:,:,1) and (:,:,2), the imwarp operation doesn't give me a correlated displacement. For instance, if the x and y displacement fields are identical (say, create a radial displacement field and compute 45 degree x and y components), I expect the displacements to be diagonal because both x and y displacement for each pixel is identical. However, what I get is a displacement in x and y independently.

I searched the image processing documentation but I can't seem to find any way to do what I want.