Title: Compression without Quantization. Abstract:  Standard compression algorithms work by mapping an image to discrete code using an encoder from which the original image can be reconstructed through a decoder. This process, due to the quantization step, is inherently non-differentiable so these algorithms must rely on approximate methods to train the encoder and decoder end-to-end. In this paper, we present an innovative framework for lossy image compression which is able to circumvent the quantization step by relying on a non-deterministic compression codec. The decoder maps the input image to a distribution in continuous space from which a sample can be encoded with expected code length being the relative entropy to the encoding distribution, i.e. it is bits-back efficient. The result is a principled, end-to-end differentiable compression framework that can be straight-forwardly trained using standard gradient-based optimizers. To showcase the efficiency of our method, we apply it to lossy image compression by training Probabilistic Ladder Networks (PLNs) on the CLIC 2018 dataset and show that their rate-distortion curves on the Kodak dataset are competitive with the state-of-the-art on low bitrates.