  Unintegrated gluon distributions sensitive to the transverse spatial
distribution of gluons in the proton are extracted from data on exclusive and
diffractive final states at HERA in the dipole approach. These unintegrated
gluon distributions can be used to compute inclusive hadron production in p+p
collisions at the LHC. In this paper, we consider a number of saturation models
with differering dynamical assumptions that give good fits to the available
HERA data. We apply these models to study the rapidity and transverse momentum
dependence of the LHC data up to $\sqrt{s} = 7$ TeV. We examine the sensitivity
of these results to parameters that are not constrained by the HERA data and
comment on similarities and differences with previous work. We compute the
n-particle inclusive multiplicity distribution and show that the LHC p+p
results are in agreement with predictions for multi-particle production in the
Color Glass Condensate approach. This result has significant ramifications for
the interpretation of multi-particle correlations in high multiplicity events
at the LHC.
