On the Inverse Flow Matching Problem in the One-Dimensional and Gaussian Cases
This addresses a theoretical gap in generative AI applications, such as model distillation, but is incremental as it focuses on specific cases.
The paper tackles the inverse problem of flow matching between distributions with finite exponential moment, establishing uniqueness of the solution in the one-dimensional and Gaussian cases, while leaving the general multidimensional problem open.
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.