  We consider image sets of differentially $d$-uniform maps of finite fields.
We present a lower bound on the image size of such maps and study their
preimage distribution, by extending methods used for planar maps. We apply the
results to study $d$-uniform Dembowski-Ostrom polynomials. Further, we focus on
a particularly interesting case of APN maps on binary fields. We show that APN
maps with the minimal image size must have a very special preimage
distribution. We prove that for an even $n$ the image sets of several
well-studied families of APN maps are minimal. We present results connecting
the image sets of special maps with their Walsh spectrum. Especially, we show
that the fact that several large classes of APN maps have the classical Walsh
spectrum is explained by the minimality of their image sets. Finally, we
present upper bounds on the image size of APN maps.
