  Cross-domain mapping has been a very active topic in recent years. Given one
image, its main purpose is to translate it to the desired target domain, or
multiple domains in the case of multiple labels. This problem is highly
challenging due to three main reasons: (i) unpaired datasets, (ii) multiple
attributes, and (iii) the multimodality (e.g., style) associated with the
translation. Most of the existing state-of-the-art has focused only on two
reasons, i.e. either on (i) and (ii), or (i) and (iii). In this work, we
propose a joint framework (i, ii, iii) of diversity and multi-mapping
image-to-image translations, using a single generator to conditionally produce
countless and unique fake images that hold the underlying characteristics of
the source image. Our system does not use style regularization, instead, it
uses an embedding representation that we call domain embedding for both domain
and style. Extensive experiments over different datasets demonstrate the
effectiveness of our proposed approach in comparison with the state-of-the-art
in both multi-label and multimodal problems. Additionally, our method is able
to generalize under different scenarios: continuous style interpolation,
continuous label interpolation, and fine-grained mapping. Code and pretrained
models are available at https://github.com/BCV-Uniandes/SMIT.
