  Classical Cepheids are the archetype of the standard candle, thanks to the
period-luminosity relation which allows to measure their intrinsic brightness.
They are also relatively young and bright, potentially making them excellent
tracers of the young stellar population that is responsible for shaping the
visible aspect of our Galaxy, the Milky Way. However, being observers embedded
in the dusty interstellar medium of the Galaxy, deriving reliable photometric
distances to classical Cepheids of the Milky Way is a challenge. The typical
approach is to use reddening-free indices, such as Wesenheit magnitudes, to
obviate the need for an extinction correction. However, this approach is not
reliable - especially toward the inner Galaxy - as its assumption of a
universal total-to-selective extinction ratio is not satisfied, particularly in
lines-of-sight where the extinction is high and crosses spiral arms. We instead
estimate new distances for 3425 Cepheids based on mid-IR photometry from WISE,
which suffers minimally from extinction, and by adopting a 3D extinction map to
calculate the necessary (albeit small) extinction corrections. We show that our
distances are consistent with Gaia's parallaxes for the subset with relative
parallax errors smaller than 10%, verifying that our mean distance errors are
of the order of 13% and that the mean parallax zero point for this subsample is
7 $\mu$as. The catalog of Cepheid distances is made available online.
