  We present a novel Monte-Carlo implementation of dynamic colour screening via
multiple exchanges of semi-soft gluons as a basic QCD mechanism to understand
diffractive electron-proton scattering at the HERA collider. Based on the
kinematics of individual events in the standard QCD description of deep
inelastic scattering at the parton level, which at low $x$ is dominantly
gluon-initiated, the probability is evaluated for additional exchanges of
softer gluons resulting in an overall colour singlet exchange leading to a
forward proton and a rapidity gap as the characteristic observables for
diffractive scattering. The probability depends on the impact parameter of the
soft exchanges and varies with the transverse size of the hard scattering
subsystem and is therefore influenced by different QCD effects. We account for
matrix elements and parton shower evolution either via conventional DGLAP $\log
Q^2$-evolution with collinear factorisation or CCFM small-$x$ evolution with
$k_\perp$-factorisation and discuss the sensitivity to the gluon density
distribution in the proton and the importance of large log\,$x$-contributions.
The overall result is that, with only two model parameters which have
theoretically motivated values, a satisfactory description of the observed
diffractive cross-section at HERA is obtained in a wide kinematical range.
