  The Gaia colour--magnitude diagram reveals a striking separation between
hydrogen-atmosphere white dwarfs and their helium-atmosphere counterparts
throughout a significant portion of the white dwarf cooling track. However,
pure-helium atmospheres have Gaia magnitudes that are too close to the
pure-hydrogen case to explain this bifurcation. To reproduce the observed split
in the cooling sequence, it has been shown that trace amounts of hydrogen
and/or metals must be present in the helium-dominated atmospheres of
hydrogen-deficient white dwarfs. Yet, a complete explanation of the Gaia
bifurcation that takes into account known constraints on the spectral evolution
of white dwarfs has thus far not been proposed. In this work, we attempt to
provide such a holistic explanation by performing population synthesis
simulations coupled with state-of-the-art model atmospheres and evolutionary
calculations that account for element transport in the envelopes of white
dwarfs. By relying on empirically grounded assumptions, these simulations
successfully reproduce the bifurcation. We show that the convective dredge-up
of optically undetectable traces of carbon from the deep interior is crucial to
account for the observations. Neither the convective dilution/mixing of
residual hydrogen nor the accretion of hydrogen or metals can be the dominant
drivers of the bifurcation. Finally, we emphasize the importance of improving
theoretical models for the average ionization level of carbon in warm dense
helium, which governs the shape of the diffusive tail of carbon and in turn the
predicted amount of dredged-up carbon.
