Convergence rates for generative drifting flows: fixed-scale obstructions and multihead acceleration
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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BibTeX
@misc{stephanovitch2026convergence,
title = {{Convergence rates for generative drifting flows: fixed-scale obstructions and multihead acceleration}},
author = {Arthur Stéphanovitch and Eddie Aamari},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05760108v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Convergence rates for generative drifting flows: fixed-scale obstructions and multihead acceleration
AU - Arthur Stéphanovitch
AU - Eddie Aamari
PY - 2026
DA - 2026/09/23
PB - HAL
UR - https://hal.science/hal-05760108v1
AB - 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.
ER -