  Image translation across different domains has attracted much attention in
both machine learning and computer vision communities. Taking the translation
from source domain $\mathcal{D}_s$ to target domain $\mathcal{D}_t$ as an
example, existing algorithms mainly rely on two kinds of loss for training: One
is the discrimination loss, which is used to differentiate images generated by
the models and natural images; the other is the reconstruction loss, which
measures the difference between an original image and the reconstructed version
through $\mathcal{D}_s\to\mathcal{D}_t\to\mathcal{D}_s$ translation. In this
work, we introduce a new kind of loss, multi-path consistency loss, which
evaluates the differences between direct translation
$\mathcal{D}_s\to\mathcal{D}_t$ and indirect translation
$\mathcal{D}_s\to\mathcal{D}_a\to\mathcal{D}_t$ with $\mathcal{D}_a$ as an
auxiliary domain, to regularize training. For multi-domain translation (at
least, three) which focuses on building translation models between any two
domains, at each training iteration, we randomly select three domains, set them
respectively as the source, auxiliary and target domains, build the multi-path
consistency loss and optimize the network. For two-domain translation, we need
to introduce an additional auxiliary domain and construct the multi-path
consistency loss. We conduct various experiments to demonstrate the
effectiveness of our proposed methods, including face-to-face translation,
paint-to-photo translation, and de-raining/de-noising translation.
