Adapting Noise to Data: Generative Flows from 1D Processes
Machine Learning
2026-02-11 v4 Machine Learning
Analysis of PDEs
Abstract
The default Gaussian latent in flow-based generative models poses challenges when learning certain distributions such as heavy-tailed ones. We introduce a general framework for learning data-adaptive latent distributions using one-dimensional quantile functions, optimized via the Wasserstein distance between noise and data. The quantile-based parameterization naturally adapts to both heavy-tailed and compactly supported distributions and shortens transport paths. Numerical results confirm the method's flexibility and effectiveness achieved with negligible computational overhead.
Cite
@article{arxiv.2510.12636,
title = {Adapting Noise to Data: Generative Flows from 1D Processes},
author = {Jannis Chemseddine and Gregor Kornhardt and Richard Duong and Gabriele Steidl},
journal= {arXiv preprint arXiv:2510.12636},
year = {2026}
}