Transition Flow Matching

TL;DR

This paper introduces a novel approach called Transition Flow Matching that directly learns transition flows, enabling efficient, single-step generation at arbitrary times, and unifies with Mean Velocity Flow models through a solid theoretical framework.

Contribution

It proposes a new paradigm for flow modeling that directly learns transition flows, simplifying generation and unifying with existing mean velocity models.

Findings

Effective single-step generation at arbitrary times.

Theoretical connection between transition flow and mean velocity flow.

Experimental results validate the approach's effectiveness.

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.