Title: Vector Quantized Wasserstein Auto-Encoder. Abstract: Learning deep discrete latent presentations offers a promise of better symbolic and summarized abstractions that are more useful to subsequent downstream tasks. Recent work on Vector Quantized Variational Auto-Encoder (VQ-VAE) has made substantial progress in this direction. However, this quantizes latent representations using the online k-means algorithm which suffers from poor initialization and non-stationary clusters. To strengthen the clustering quality for the latent representations, we propose Vector Quantized Wasserstein Auto-Encoder (VQ-WAE) intuitively developed based on the clustering viewpoint of Wasserstein (WS) distance. Specifically, we endow a discrete distribution over the codewords and learn a deterministic decoder that transports the codeword distribution to the data distribution via minimizing a WS distance between them. We develop further theories to connect it with the clustering viewpoint of WS distance, allowing us to have a better and more controllable clustering solution. Finally, we empirically evaluate our method on several well-known benchmarks, where it achieves better qualitative and quantitative performances than the baselines in terms of the codebook utilization and image reconstruction/generation.