We show that the recently developed Hamiltonian theory for high energy evolution in QCD in the dilute regime and in the presence of Bremsstrahlung is consistent with the color dipole picture in the limit where the number of colors N_c is large. The color dipoles are quark-antiquark pairs which can radiate arbitrarily many soft gluons, and the evolution consists in the splitting of any such a dipole into two. We construct the color glass weight function of an onium as a superposition of color dipoles, each represented by a pair of Wilson lines. We show that the action of the Bremsstrahlung Hamiltonian on this weight function and in the large-N_c limit generates the evolution expected from the dipole picture. We construct the dipole number operator in the Hamiltonian theory and deduce the evolution equations for the dipole densities, which are again consistent with the dipole picture. We argue that the Bremsstrahlung effects beyond two gluon emission per dipole are irrelevant for the calculation of scattering amplitudes at high energy.
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