  The proton diffractive structure function $F_2^{D(3)}$ measured in the H1 and
ZEUS experiments at HERA is analyzed in terms of both Regge phenomenology and
perturbative QCD evolution. A new method determines the values of the Regge
intercepts in ``hard'' diffraction, confirming a higher value of the Pomeron
intercept than for soft physics. The data are well described by a QCD analysis
in which point-like parton distributions, evolving according to the DGLAP
equations, are assigned to the leading and sub-leading Regge exchanges. The
gluon distributions are found to be quite different for H1 and ZEUS. A {\it
global fit} analysis, where a higher twist component is taken from models,
allows us to use data in the whole available range in diffractive mass and
gives a stable answer for the leading twist contribution. We give sets of quark
and gluon parton distributions for the Pomeron, and predictions for the charm
and the longitudinal proton diffractive structure function from the QCD fit. An
extrapolation to the Tevatron range is compared with CDF data on single
diffraction. Conclusions on factorization breaking depend critically whether H1
(strong violation) or ZEUS (compatibility at low $\beta$) fits are taken into
account.
