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Abstract: Abstract Traffic flow distribution forecasting plays a crucial role in intelligent transportation systems for effective traffic management and congestion mitigation. In this paper, we propose a novel approach for traffic flow distribution forecasting using federated learning and Bayesian deep learning. The proposed method leverages the collaborative training capability of federated learning to learn from decentralized data sources while preserving data privacy and ownership. Bayesian deep learning techniques are integrated to estimate uncertainties and provide probabilistic predictions, enabling the capture of the inherent variability in traffic flow distributions. We conduct comprehensive experiments on real-world traffic flow datasets and compare our method with baseline approaches. The results demonstrate that our proposed method outperforms the baselines in terms of mean absolute error, root mean squared error, negative log-likelihood, and calibration error. The integration of federated learning and Bayesian deep learning enables accurate traffic flow distribution forecasts while providing reliable uncertainty estimates. This work contributes to the advancement of intelligent transportation systems and provides valuable insights for decision-making in traffic management and congestion reduction.