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=== Optimal transport flow ===
The idea of '''optimal transport flow''' <ref>{{Cite journal |last1=Tong |first1=Alexander |last2=Fatras |first2=Kilian |last3=Malkin |first3=Nikolay |last4=Huguet |first4=Guillaume |last5=Zhang |first5=Yanlei |last6=Rector-Brooks |first6=Jarrid |last7=Wolf |first7=Guy |last8=Bengio |first8=Yoshua |date=2023-11-08 |title=Improving and generalizing flow-based generative models with minibatch optimal transport |url=https://openreview.net/forum?id=CD9Snc73AW |journal=Transactions on Machine Learning Research |arxiv=2302.00482 |language=en |issn=2835-8856}}</ref> is to construct a probability path minimizing the [[Wasserstein metric]]. The distribution on which we condition is an approximation of the optimal transport plan between <math>\pi_0 </math> and <math>\pi_1
</math>: <math>z = (x_0, x_1) </math> and <math>q(z) = \Gamma(\pi_0, \pi_1) </math>, where <math>\Gamma</math> is the optimal transport plan, which can be approximated by '''mini-batch optimal transport.''' If the batch size is not large, then the transport it computes can be very far from the true optimal transport.
=== Rectified flow ===
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