On the Stability and Convergence of Flow Map Training

The paper investigates the training dynamics of flow map models, which convert diffusion trajectories into one‑step samplers for efficient probabilistic generation. It provides a theoretical analysis of the functional gradient flow induced by MeanFlow and Lagrangian losses, proving their convergence to the true flow map and identifying the risk of unbounded updates. The authors show that adaptive normalization and a specific reweighting scheme not only bound updates but also guarantee convergence to a neighborhood of the solution, and they confirm these findings with synthetic experiments and image‑generation benchmarks.

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• diffusion