{"ID":2824242,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.23265","arxiv_id":"2512.23265","title":"On the Inverse Flow Matching Problem in the One-Dimensional and Gaussian Cases","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.","short_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 Gauss...","url_abs":"https://arxiv.org/abs/2512.23265","url_pdf":"https://arxiv.org/pdf/2512.23265v1","authors":"[\"Alexander Korotin\",\"Gudmund Pammer\"]","published":"2025-12-29T07:45:36Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}