Advection-dominated fluid dynamics problems are commonly known to be particularly challenging in terms of Reduced Order Modelling (ROM). Unfortunately, advection-dominated problems are also frequently encountered in many fields of engineering interest, from turbulent flows to wave propagation, acoustics, and compressible single- and multi-phase problems. The present work is focused on using optimal transport displacement interpolation [1] to enhance model order reduction for these problems. The methodology developed in [2] is applied to two-phase flows, which fall into the larger set of advection-dominated flows. In particular, the full-order model used to generate the data for model order reduction is based on a high-order spectral difference discretisation of a diffused interface formulation of the five- equation model [3]. Optimal transport theory can represent an interesting avenue for non-linear reduced order modelling, alleviating the slow-decaying Kolmogorov width typical of advection-dominated flows. From a methodological point of view, as a first option, the optimal transport framework has been used as a tool for data augmentation, which can then be immediately used within relatively standard reduced order modelling strategies (i.e., POD-based methods). Although this strategy is still intrinsically linear, it avoids storing a large amount of data needed for linear ROMs by simply creating new ones in a more efficient way. More sophisticated strategies, instead, can take advantage of the displacement interpolation in order to correct low-dimensional POD-based ROMs, introducing implicit non-linearity through the displacement interpolation map. Both kinematic and fully coupled two-phase flows are considered in this work. An example of the proposed methodology applied to a parametrised Rider–Kothe vortex test case is shown in Figure 1.