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Flow-based generative models trained with flow matching tend to learn curved trajectories, which are challenging to approximate in a few steps. Rectified flows aim to learn straight trajectories, which are easier to simulate with less computation.

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Alec Helbling

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In flow matching, a coupling determines how noise and data samples are paired during training. The choice of coupling is important because it influences the geometry of trajectories at inference time. The simplest choice is the independent coupling, where noise and data points are paired arbitrarily. This can lead to curved trajectories as the model averages over many conflicting pairings. However, if we use optimal transport on batches of pairs, this leads to fewer ambiguous intersections that the model must resolve, leading to straighter trajectories at inference time.
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