Title: A Sampling-Free Approximation of Gaussian Variational Auto-Encoders. Abstract: We propose a sampling-free approximate formulation of Gaussian variational auto-encoders. Instead of computing the loss via stochastic sampling, we propagate the Gaussian distributions from the latent space into the output space. As computing the exact likelihood probability is intractable, we propose to locally approximate the decoder network by its Taylor series. We demonstrate that this approximation allows us to approximate the Gaussian variational auto-encoder training objective in closed form. We evaluate the proposed method on the CelebA, the 3D Chairs, and the MNIST data sets. We find that our sampling-free approximation performs better than its sampling counterpart on the Frechet inception distance and on par on the estimated marginal likelihood.