Broadening of the transverse momentum of a parton propagating through a medium is treated using the color dipole formalism, which has the advantage of being a well developed phenomenology in deep-inelastic scattering and soft processes. Within this approach, nuclear broadening should be treated as color filtering, i.e. absorption of large-size dipoles leading to diminishing (enlarged) transverse separation (momentum). We also present a more intuitive derivation based on the classic scattering theory of Moli`ere. This derivation helps to understand the origin of the dipole cross section, part of which comes from attenuation of the quark, while another part is due to multiple interactions of the quark. It also demonstrates that the lowest-order rescattering term provides an A-dependence very different from the generally accepted A^{1/3} behavior. The effect of broadening increases with energy, and we evaluate it using different phenomenological models for the unintegrated gluon density. Although the process is dominated by soft interactions, the phenomenology we use is tested using hadronic cross section data.
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