Federated Learning (FL) provides a framework for collaborative training of deep learning models while preserving data privacy by avoiding sharing the training data. However, recent studies have shown that a malicious server can reconstruct training data from the shared gradients of traditional neural networks (NNs) in FL, via Gradient Inversion Attacks (GIAs) that emulate the client's training process. Contrary to earlier beliefs that Stochastic Neural Networks (SNNs) are immune to such attacks due to their stochastic nature (which makes the training process challenging to mimic), our findings reveal that SNNs are equally susceptible to GIAs as SNN gradients contain the information of stochastic components, allowing attackers to reconstruct and disclose those uncertain components. In this work, we play the role of an attacker and propose a novel attack method, named Inverting Stochasticity from Gradients (ISG), that can successfully reconstruct the training data by formulating the stochastic training process of SNNs as a variant of the traditional NN training process. Furthermore, to improve the fidelity of the reconstructed data, we introduce a feature constraint strategy. Extensive experiments validate the effectiveness of our GIA and suggest that perturbation-based defenses in forward propagation, such as using SNNs, fail to secure models against GIAs inherently. The source code of our work will be made available to the public on GitHub.