Title: Tailoring Noise to Data: Generative Flows Driven by 1D Processes

Abstract: Employing standard Gaussian latents in flow-based generative models often creates difficulties when attempting to learn specific distributions, particularly those with heavy tails. To address this, we propose a comprehensive framework that learns data-adaptive parametric prior distributions—effectively the latent noise—by leveraging one-dimensional quantile functions. This optimization process relies on minimizing the Wasserstein distance between the noise and the data. By parameterizing the prior through quantiles, the model inherently accommodates both compactly supported and heavy-tailed distributions, thereby reducing the length of transport paths. Empirical evaluations on heavy-tailed image and weather datasets demonstrate that this approach offers significant flexibility and effectiveness, all while incurring minimal computational cost.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC