Adapting Noise to Data by Quantile Learning

The common assumption of a Gaussian latent space in flow-based generative models can be restrictive, especially when modeling heavy-tailed data distributions. To better accommodate complex data geometries, we propose learning data-adaptive latent distributions via one-dimensional quantile functions. These are trained by minimizing the Wasserstein distance between noise and data. Thereby, the latent adapts to both heavy-tailed and compactly supported distributions while shortening transport paths. Numerical results confirm the method’s flexibility and effectiveness achieved with negligible computational overhead.