Abstract: A traditional deep neural network can achieve a high-precision deterministic inversion of acoustic impedance, without uncertainty analysis of the results.This means that the reliability of the inversion cannot be evaluated.To solve this problem, a novel approach called dual Bayesian U-Net is proposed for acoustic impedance uncertainty inversion.This method performs well in the context of a small number of labels.Moreover, it realizes uncertainty analysis on inversion results.The experiments on synthetic data demonstrate that dual Bayesian U-Net could rival additional deep neural networks in the accuracy of inversion and is superior to traditional uncertainty inversion methods in accuracy, robustness, and reliability, particularly for noisy data.Field data tests show that the proposed method can obtain reasonable and reliable inversion results.