Transition Flow Matching

arXiv cs.LG / 3/18/2026

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Key Points

The paper proposes Transition Flow Matching, a paradigm that directly learns the transition flow as a global quantity to enable one-shot or arbitrary-time generation.
It contrasts with mainstream flow matching methods that learn the local velocity field and require multiple integration steps during generation, and it establishes a theoretical connection to Mean Velocity Flow.
The authors present a unified theoretical perspective linking transition flow and mean velocity flow and support their claims with extensive experiments.
By enabling generation at arbitrary future time points, the approach could simplify and accelerate flow-based generative modeling workflows.

Abstract

Mainstream flow matching methods typically focus on learning the local velocity field, which inherently requires multiple integration steps during generation. In contrast, Mean Velocity Flow models establish a relationship between the local velocity field and the global mean velocity, enabling the latter to be learned through a mathematically grounded formulation and allowing generation to be transferred to arbitrary future time points. In this work, we propose a new paradigm that directly learns the transition flow. As a global quantity, the transition flow naturally supports generation in a single step or at arbitrary time points. Furthermore, we demonstrate the connection between our approach and Mean Velocity Flow, establishing a unified theoretical perspective. Extensive experiments validate the effectiveness of our method and support our theoretical claims.