Image reconstructions involving neural networks (NNs) are generally non-iterative and computationally efficient. However, without analytical expression describing the reconstruction process, the compuation of noise propagation becomes difficult. Automated differentiation allows rapid computation of derivatives without an analytical expression. In this work, the feasibility of computing noise propagation with automated differentiation was investigated. The noise propagation of image reconstruction by End-to-end variational-neural-network was estimated using automated differentiation and compared with Monte-Carlo simulation. The root-mean-square error (RMSE) map showed great agreement between automated differentiation and Monte-Carlo simulation over a wide range of SNRs.