Abstract: Autoregressive models (ARMs) currently hold state-of-the-art performance in likelihood-based modeling of image and audio data. Generally, neural network based ARMs are designed to allow fast inference, but sampling from these models is impractically slow. In this paper, we introduce the predictive sampling algorithm: a procedure that exploits the fast inference property of ARMs in order to speed up sampling, while keeping the model intact. We propose two variations of predictive sampling, namely sampling with ARM fixed-point iteration and learned forecasting modules. Their effectiveness is demonstrated in two settings: i) explicit likelihood modeling on binary MNIST, SVHN and CIFAR10, and ii) discrete latent modeling in an autoencoder trained on SVHN, CIFAR10 and Imagenet32. Empirically, we show considerable improvements over baselines in number of ARM inference calls and sampling speed.