On the Inverse Flow Matching Problem in the One-Dimensional and Gaussian Cases
On the map: Diffusion models → Flow matching, time series and science
Abstract (arXiv)
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.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 3 of its 5 references that are in the map. First posted on arXiv 29 Dec 2025.
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3 of 5 references.
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- 2024Flow Generator Matching25 Oct
- 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep
Other references · 1
- 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesiscited by 4,181
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