  In this paper, we explore the appealing possibility that the strong
suppression of large-size QCD instantons - as evident from lattice data - is
due to a surviving conformal space-time inversion symmetry. This symmetry is
both suggested from the striking invariance of high-quality lattice data for
the instanton size distribution under inversion of the instanton size rho -->
<rho>^2 / rho and from the known validity of space-time inversion symmetry in
the classical instanton sector. We project the instanton calculus onto the
four-dimensional surface of a five-dimensional sphere via conformal
stereographic mapping, before investigating conformal inversion. This
projection to a compact, curved geometry is both to avoid the occurence of
divergences and to introduce the average instanton size <rho> from the lattice
data as a new length scale. The average instanton size is identified with the
radius b of this 5d-sphere and acts as the conformal inversion radius. For b =
<rho>, our corresponding results are almost perfectly symmetric under
space-time inversion and in good qualitative agreement with the lattice data.
For rho / b --> 0, we recover the familiar results of instanton perturbation
theory in flat 4d-space. Moreover, we illustrate that a (weakly broken)
conformal inversion symmetry would have significant consequences for QCD beyond
instantons. As a further successful test for inversion symmetry, we present
striking implications for another instanton dominated lattice observable, the
chirality-flip ratio in the QCD vacuum.
