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However, acquiring paired data samples is often challenging, especially in problems such as domain translation. This necessitates the development of $\\textit{semi-supervised}$ models that utilize both limited paired data and additional unpaired i.i.d. samples $x \\sim \\pi^*_x$ and $y \\sim \\pi^*_y$ from the marginal distributions. The usage of such combined data is complex and often relies on heuristic approaches. To tackle this issue, we propose a new learning paradigm called $\\textbf{EBiEOT}$ that integrates both paired and unpaired data seamlessly using data likelihood maximization techniques. We demonstrate that our approach also connects intriguingly with inverse entropic optimal transport (OT). 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