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

• URL: http://arxiv.org/abs/2512.23265v1
• Date: Mon, 29 Dec 2025 07:45:36 GMT
• Title: On the Inverse Flow Matching Problem in the One-Dimensional and Gaussian Cases
• Authors: Alexander Korotin, Gudmund Pammer,
• Abstract summary: This paper studies the inverse problem of flow matching (FM) between distributions with finite exponential moment.<n>It is motivated by modern generative AI applications such as the distillation of flow matching models.
• Score: 58.228512978259026
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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