On the Equivalence of Optimal Transport Problem and Action Matching with Optimal Vector Fields

arXiv — cs.LGMonday, November 3, 2025 at 5:00:00 AM

On the Equivalence of Optimal Transport Problem and Action Matching with Optimal Vector Fields

A recent study has explored the relationship between the Flow Matching (FM) method in generative modeling and the Optimal Transport Problem, revealing that FM can be adapted to achieve optimal mapping of probability distributions. This is significant as it enhances our understanding of how to efficiently interpolate between distributions using specific optimal vector fields, which could have implications for various applications in machine learning and data analysis.
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