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arXiv · 2609.15193

Convergence rates for generative drifting flows: fixed-scale obstructions and multihead acceleration

Arthur Stéphanovitch·Eddie Aamari
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Abstract

Drifting models offer a promising route to faster generative AI: they perform gradual transport during training, while generating new samples in a single step. This paper asks whether the underlying drifting process can converge rapidly to a target distribution under ideal conditions, before finite-data or optimization effects are introduced. We show that its convergence rate depends critically on how it handles spatial scale. With a single fixed resolution, fine-scale features of the target can become nearly invisible, leading to extremely slow convergence. We introduce a multihead approach that combines scale-normalized information across a continuum of resolutions. We prove that this multihead approach restores exponential convergence near standard reference distributions. These results identify fixed resolution as a key bottleneck and provide a simple route to faster one-step generative models.

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Arthur Stéphanovitch, Eddie Aamari. 2026-09-14. Convergence rates for generative drifting flows: fixed-scale obstructions and multihead acceleration. https://arxiv.org/abs/2609.15193

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