{"ID":2855818,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.12636","arxiv_id":"2510.12636","title":"Adapting Noise to Data: Generative Flows from 1D Processes","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.","short_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...","url_abs":"https://arxiv.org/abs/2510.12636","url_pdf":"https://arxiv.org/pdf/2510.12636v4","authors":"[\"Jannis Chemseddine\",\"Gregor Kornhardt\",\"Richard Duong\",\"Gabriele Steidl\"]","published":"2025-10-14T15:30:28Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"math.AP\"]","methods":"[]","has_code":false}