arXiv:2604.00673v3 Announce Type: replace Abstract: Probabilistic power flow (PPF) is essential for quantifying operational uncertainty in modern power systems with high penetrations of renewable generation and flexible loads. Conventional PPF methods primarily rely on Monte Carlo (MC)based power flow (PF) simulations or simplified approximations of voltage probability density functions. Although MC methods provide high accuracy, they incur substantial computational and data-storage costs, whereas simplified approximations, though lightweight, often sacrifice accuracy due to the reliance of certain assumption. In this paper, we propose a novel PPF density approximation framework that leverages the expressive power of neural networks (NNs) and can, in principle, approximate complex voltage distributions directly without restrictive assumptions. The core idea is to learn an explicit mapping between stochastic power injections and system voltages using invertible neural networks (INNs), and then to apply the change-of-variables theorem to obtain the voltage densities. Extensive numerical studies demonstrate that the proposed framework achieves stateof-the-art performance both as an accurate PF solver and as an efficient PPF density estimator