ICML 2026poster0 citations
Learning Manifold Data with Flow Matching
Sophia Pi, Mingcheng Lu, Jerry Yao-Chieh Hu, Maojiang Su, Weimin Wu, Han Liu
Abstract
We study flow-matching transformers when data lie on a low-dimensional manifold. Our key insight is a flow decomposition that splits motion along the manifold from motion off the manifold. The scheme works for first- and higher-order flow matching and ties model complexity to the intrinsic manifold dimension. Building on these, we establish tighter sample-complexity bounds for velocity approximation, velocity estimation, and distribution estimation. These bounds meet near-minimax rates for flow-matching transformers of any order. Our results show how flow-matching transformers escape the curse of dimensionality by utilizing intrinsic data structure.
TransformerTheory
BibTeX
@inproceedings{
pi2026learning,
title={Learning Manifold Data with Flow Matching},
author={Sophia Pi and Mingcheng Lu and Maojiang Su and Weimin Wu and Jerry Yao-Chieh Hu and Han Liu},
booktitle={Forty-third International Conference on Machine Learning},
year={2026},
url={https://openreview.net/forum?id=9mA5d705Gd}
}