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m Undid revision. InDI citation is reliable and very connected to the other mentioned work (Flow Matching, alpha deblending, stochastic interpolants). The paper was published in TMLR and received an outstanding award. The math formulation is conceptually the same but was independently introduced. See: https://medium.com/@TmlrOrg/announcing-the-2024-tmlr-outstanding-certification-65f25d05c37c Tag: Reverted |
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<math display="block">\min_{\theta} \int_0^1 \mathbb{E}_{\pi_0, \pi_1, p_t}\left [\lVert{(x_1-x_0) - v_t(x_t)}\rVert^2\right] \,\mathrm{d}t.</math>
The data pair <math>(x_0, x_1)</math> can be any coupling of <math>\pi_0</math> and <math>\pi_1</math>, typically independent (i.e., <math>(x_0,x_1) \sim \pi_0 \times \pi_1</math>) obtained by randomly combining observations from <math>\pi_0</math> and <math>\pi_1</math>. This process ensures that the trajectories closely mirror the density map of <math>x_t</math> trajectories but ''reroute'' at intersections to ensure causality. This rectifying process is also known as Flow Matching,<ref>{{cite arXiv |last1=Lipman |first1=Yaron |title=Flow Matching for Generative Modeling |date=2023-02-08 |eprint=2210.02747 |last2=Chen |first2=Ricky T. Q. |last3=Ben-Hamu |first3=Heli |last4=Nickel |first4=Maximilian |last5=Le |first5=Matt|class=cs.LG }}</ref> Stochastic Interpolation,<ref>{{cite arXiv |last1=Albergo |first1=Michael S. |title=Building Normalizing Flows with Stochastic Interpolants |date=2023-03-09 |eprint=2209.15571 |last2=Vanden-Eijnden |first2=Eric|class=cs.LG
[[File:Reflow Illustration.png|thumb|390px|The reflow process<ref name=":0"/>]]
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