<ul><li>Flow Matching (FM) is a generative modelling technique that aims to learn how to sample from a target distribution by flowing samples from an easy-to-sample distribution.</li><li>Existing FM methods use straight line segments or geodesics for flow matching, but they are only well-defined on Euclidean space or Riemannian manifolds.</li><li>The alternative approach in this work is to apply FM on Lie groups by using exponential curves instead of straight line segments, leading to a simple and fast implementation using matrix operations.</li><li>FM on Lie groups can be used for generative modelling with data consisting of sets of features and poses.</li></ul>

Flow Matching on Lie Groups

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