Adapting Noise to Data: Generative Flows from Learned 1D Processes

Jannis Chemseddine, Gregor Kornhardt, Richard Duong, Gabriele Steidl
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:13400-13430, 2026.

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 parametric prior distributions (latent noise) using one-dimensional quantile functions, optimized via the Wasserstein distance between noise and data. The quantile-based prior parameterization naturally adapts to both heavy-tailed and compactly supported distributions and shortens transport paths. Numerical results on heavy-tailed weather and image datasets confirm the method’s flexibility and effectiveness achieved with negligible computational overhead.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-chemseddine26a, title = {Adapting Noise to Data: Generative Flows from Learned 1{D} Processes}, author = {Chemseddine, Jannis and Kornhardt, Gregor and Duong, Richard and Steidl, Gabriele}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {13400--13430}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/chemseddine26a/chemseddine26a.pdf}, url = {https://proceedings.mlr.press/v306/chemseddine26a.html}, 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 parametric prior distributions (latent noise) using one-dimensional quantile functions, optimized via the Wasserstein distance between noise and data. The quantile-based prior parameterization naturally adapts to both heavy-tailed and compactly supported distributions and shortens transport paths. Numerical results on heavy-tailed weather and image datasets confirm the method’s flexibility and effectiveness achieved with negligible computational overhead.} }
Endnote
%0 Conference Paper %T Adapting Noise to Data: Generative Flows from Learned 1D Processes %A Jannis Chemseddine %A Gregor Kornhardt %A Richard Duong %A Gabriele Steidl %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-chemseddine26a %I PMLR %P 13400--13430 %U https://proceedings.mlr.press/v306/chemseddine26a.html %V 306 %X 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 parametric prior distributions (latent noise) using one-dimensional quantile functions, optimized via the Wasserstein distance between noise and data. The quantile-based prior parameterization naturally adapts to both heavy-tailed and compactly supported distributions and shortens transport paths. Numerical results on heavy-tailed weather and image datasets confirm the method’s flexibility and effectiveness achieved with negligible computational overhead.
APA
Chemseddine, J., Kornhardt, G., Duong, R. & Steidl, G.. (2026). Adapting Noise to Data: Generative Flows from Learned 1D Processes. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:13400-13430 Available from https://proceedings.mlr.press/v306/chemseddine26a.html.

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