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As a powerful technique in medical imaging, image synthesis is widely used in applications such as denoising, super resolution and modality transformation etc. Recently, the revival of deep neural networks made immense progress in the field of medical imaging. Although many deep leaning based models have been proposed to improve the image synthesis accuracy, the evaluation of the model uncertainty, which is highly important for medical applications, has been a missing part. In this work, we propose to use Bayesian conditional generative adversarial network (GAN) with concrete dropout to improve image synthesis accuracy. Meanwhile, an uncertainty calibration approach is involved in the whole pipeline to make the uncertainty generated by Bayesian network interpretable. The method is validated with the T1w to T2w MR image translation with a brain tumor dataset of 102 subjects. Compared with the conventional Bayesian neural network with Monte Carlo dropout, results of the proposed method reach a significant lower RMSE with a p-value of 0.0186. Improvement of the calibration of the generated uncertainty by the uncertainty recalibration method is also illustrated.