🤖 AI Summary
研究探讨了生成漂移流的收敛速度问题，提出了一种多头方法来处理不同尺度的信息，从而恢复指数级收敛速度，解决了固定分辨率导致的慢收敛问题。
📝 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.