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arXiv · 2512.23265

On the Inverse Flow Matching Problem in the One-Dimensional and Gaussian Cases

Alexander Korotin·Gudmund Pammer
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Abstract

This paper studies the inverse problem of flow matching (FM) between distributions with finite exponential moment, a problem motivated by modern generative AI applications such as the distillation of flow matching models. Uniqueness of the solution is established in two cases - the one-dimensional setting and the Gaussian case. The general multidimensional problem remains open for future studies.

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Alexander Korotin, Gudmund Pammer. 2025-12-29. On the Inverse Flow Matching Problem in the One-Dimensional and Gaussian Cases. https://doi.org/10.4213/rm10283

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