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We present a coupled Variational Auto-Encoder (VAE) method that improves the accuracy and robustness of the probabilistic inferences on represented data. The new method models the dependency between input feature vectors (images) and weighs the outliers with a higher penalty by generalizing the original loss function to the coupled entropy function, using the principles of nonlinear statistical coupling. We evaluate the performance of the coupled VAE model using the MNIST dataset. Compared with the traditional VAE algorithm, the output images generated by the coupled VAE method are clearer and less blurry. The visualization of the input images embedded in 2D latent variable space provides a deeper insight into the structure of new model with coupled loss function: the latent variable has a smaller deviation and the output values are generated by a more compact latent space. We analyze the histograms of probabilities for the input images using the generalized mean metrics, in which increased geometric mean illustrates that the average likelihood of input data is improved. Increases in the -2/3 mean, which is sensitive to outliers, indicates improved robustness. The decisiveness, measured by the arithmetic mean of the likelihoods, is unchanged and -2/3 mean shows that the new model has better robustness.