Title: Smooth image-to-image translations with latent space interpolations. Abstract: Multi-domain image-to-image (I2I) translations can transform a source image according to the style of a target domain. One important, desired characteristic of these transformations, is their graduality, which corresponds to a smooth change between the source and the target image when their respective latent-space representations are linearly interpolated. However, state-of-the-art methods usually perform poorly when evaluated using inter-domain interpolations, often producing abrupt changes in the appearance or non-realistic intermediate images. In this paper, we argue that one of the main reasons behind this problem is the lack of sufficient inter-domain training data and we propose two different regularization methods to alleviate this issue: a new shrinkage loss, which compacts the latent space, and a Mixup data-augmentation strategy, which flattens the style representations between domains. We also propose a new metric to quantitatively evaluate the degree of the interpolation smoothness, an aspect which is not sufficiently covered by the existing I2I translation metrics. Using both our proposed metric and standard evaluation protocols, we show that our regularization techniques can improve the state-of-the-art multi-domain I2I translations by a large margin. Our code will be made publicly available upon the acceptance of this article.