Smart Flow Matching: On The Theory of Flow Matching Algorithms with Applications

Gleb Ryzhakov, Svetlana Pavlova, Egor Sevriugov,Ivan Oseledets

CoRR(2024)

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摘要
The paper presents the exact formula for the vector field that minimizes the loss for the standard flow. This formula depends analytically on a given distribution ρ_0 and an unknown one ρ_1. Based on the presented formula, a new loss and algorithm for training a vector field model in the style of Conditional Flow Matching are provided. Our loss, in comparison to the standard Conditional Flow Matching approach, exhibits smaller variance when evaluated through Monte Carlo sampling methods. Numerical experiments on synthetic models and models on tabular data of large dimensions demonstrate better learning results with the use of the presented algorithm.
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