Title: Outlier Preserving Distribution Mapping Autoencoders . Abstract: State-of-the-art deep outlier detection methods map data into a latent space with the aim of having  outliers far away from inliers in this space. Unfortunately, this often fails as  the divergence penalty they adopt pushes outliers into the same high-probability regions as inliers. We propose a novel method, OP-DMA, that successfully addresses the above problem. OP-DMA   succeeds in mapping outliers to low probability regions in the latent space by leveraging a novel Prior-Weighted Loss (PWL) that utilizes the insight that outliers are likely to have a higher reconstruction error than inliers. Building on this insight,  OP-DMA weights the reconstruction error of individual points by a multivariate Gaussian probability density function evaluated at each point's latent representation. We demonstrate and provide theoretical proof that this succeeds to map outliers to low-probability regions. Our experimental study shows that OP-DMA  consistently outperforms  state-of-art  methods on a rich variety of outlier detection benchmark datasets.