Different CT segmentation datasets are typically obtained from different scanners under different capture settings and often provide segmentation labels for a limited and often disjoint set of organs. Using these heterogeneous data effectively while preserving patient privacy can be challenging. This work presents a novel federated learning approach to achieve universal segmentation across diverse abdominal CT datasets by utilizing model uncertainty for aggregation and predictive uncertainty for inference. Our approach leverages the inherent noise in stochastic mini-batch gradient descent to estimate a distribution over the model weights to provide an on-the-go uncertainty over the model parameters at the client level. The parameters are then aggregated at the server using the additional uncertainty information using a Bayesian-inspired inverse-variance aggregation scheme. Furthermore, the proposed method quantifies prediction uncertainty by propagating the uncertainty from the model weights, providing confidence measures essential for clinical decision-making. In line with recent work shown, predictive uncertainty is utilized in the inference stage to improve predictive performance. Experimental evaluations demonstrate the effectiveness of this approach in improving both the quality of federated aggregation and uncertainty-weighted inference compared to previously established baselines. The code for this work is made available at: https://github.com/asimukaye/fiva