  We argue that global charges, such as baryon or lepton number, are not
conserved in theories with the Standard Model fields localized on the brane
which propagates in higher-dimensional space-time. The global-charge
non-conservation is due to quantum fluctuations of the brane surface. These
fluctuations create "baby branes" that can capture some global charges and
carry them away into the bulk of higher-dimensional space. Such processes are
exponentially suppressed at low-energies, but can be significant at high enough
temperatures or energies. These effects can lead to a new, intrinsically
high-dimensional mechanism of baryogenesis. Baryon asymmetry might be produced
due either to "evaporation" into the baby branes, or creation of the baryon
number excess in collisions of two Brane Universes. As an example we discuss a
possible cosmological scenario within the recently proposed "Brane Inflation"
framework. Inflation is driven by displaced branes which slowly fall on top of
each other. When the branes collide inflation stops and the Brane Universe
reheats. During this non-equilibrium collision baryon number can be transported
from one brane to another one. This results in the baryon number excess in our
Universe which exactly equals to the hidden "baryon number" deficit in the
other Brane Universe.
