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.

翻译：流式生成模型中默认的高斯隐变量在学习如重尾分布等特定分布时存在困难。我们提出一个通用框架，利用一维分位数函数学习数据自适应的参数化先验分布（潜噪声），并通过噪声与数据之间的Wasserstein距离进行优化。基于分位数的先验参数化能够自然地适应重尾分布和有紧支集的分布，并缩短传输路径。在重尾天气和图像数据集上的数值结果证实了该方法在计算开销极小的情况下所具备的灵活性和有效性。