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Federated learning is a machine learning paradigm that leverages edge computing on client devicesto optimize models while maintaining user privacy by ensuring that local data remain on the device.However, since all data are collected by clients, federated learning is susceptible to latent noise inlocal datasets. Factors such as limited measurement capabilities or human errors may introduce inaccuraciesin client data. To address this challenge, we propose the use of a stochastic neural networkas the local model within the federated learning framework. Stochastic neural networks not onlyfacilitate the estimation of the true underlying states of the data but also enable the quantificationof latent noise. We refer to our federated learning approach, which incorporates stochastic neuralnetworks as local models, as federated stochastic neural networks. We will present numerical experimentsdemonstrating the performance and effectiveness of our method, particularly in handlingnonindependent and identically distributed data.