Over the several recent years, there has been a boom in development of flow matching methods for generative modeling. One intriguing property pursued by the community is the ability to learn flows with straight trajectories which realize the optimal transport (OT) displacements. Straightness is crucial for fast integration of the learned flow's paths. Unfortunately, most existing flow straightening methods are based on non-trivial iterative procedures which accumulate the error during training or exploit heuristic minibatch OT approximations. To address this issue, we develop a novel optimal flow matching approach which recovers the straight OT displacement for the quadratic cost in just one flow matching step.

翻译：近年来，生成建模中的流匹配方法取得了蓬勃发展。领域内追求的一个有趣特性是学习具有直行轨迹的流，以实现最优传输（OT）位移。直线性对于快速积分所学流的路径至关重要。然而，现有的大多数流直化方法基于复杂的迭代过程，这些过程在训练期间会累积误差，或利用启发式的小批量OT近似。为了解决这一问题，我们开发了一种新颖的最优流匹配方法，该方法仅需一步流匹配即可恢复二次成本下的直行OT位移。