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arXiv · 2602.10420

Prediction--Loss Alignment for Sampler--Robust Flow Matching Training

Jiadong Hong·Lei Liu·Xinyu Bian·Wenjie Wang·Zhaoyang Zhang
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Abstract

Recent work has popularized a practical recipe in diffusion and flow matching: predict the clean signal $x$, convert it to a velocity, and train through a velocity-space loss. The conversion contains a singular endpoint amplification and therefore appears prone to unstable optimization, yet recent systems obtain strong empirical results with this recipe. We investigate this tension through the integrability of the pre-optimizer stochastic-gradient second moment. Under stated initialization conditions, the moment diverges under Uniform sampling; boundary-suppressing sampling can restore integrability under an additional upper-growth condition. We then show that prediction--loss alignment eliminates this conversion-induced source of non-integrability. Under a uniform moment bound, alignment yields a finite second moment for every timestep density, including Uniform sampling. Controlled experiments across continuous and binary settings reproduce the predicted sampler-dependent instability and show that aligned objectives remain trainable across the tested samplers. These results reconcile pointwise amplification with sampler-dependent empirical success and support alignment as a principled route to more robust flow-matching training.

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Jiadong Hong, Lei Liu, Xinyu Bian, Wenjie Wang, Zhaoyang Zhang. 2026-02-11. Prediction--Loss Alignment for Sampler--Robust Flow Matching Training. https://arxiv.org/abs/2602.10420

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