  Recent methods in modeling spatial extreme events have focused on utilizing
parametric max-stable processes and their underlying dependence structure. In
this work, we provide a unified approach for analyzing spatial extremes with
little available data by estimating the distribution of model parameters or the
spatial dependence directly. By employing recent developments in generative
neural networks we predict a full sample-based distribution, allowing for
direct assessment of uncertainty regarding model parameters or other parameter
dependent functionals. We validate our method by fitting several simulated
max-stable processes, showing a high accuracy of the approach, regarding
parameter estimation, as well as uncertainty quantification. Additional
robustness checks highlight the generalization and extrapolation capabilities
of the model, while an application to precipitation extremes across Western
Germany demonstrates the usability of our approach in real-world scenarios.
