In this paper we propose Spatial PixelCNN, a conditional autoregressive model that generates images from small patches. By conditioning on a grid of pixel coordinates and global features extracted from a Variational Autoencoder (VAE), we are able to train on patches of images, and reproduce the full-sized image. We show that it not only allows for generating high quality samples at the same resolution as the underlying dataset, but is also capable of upscaling images to arbitrary resolutions (tested at resolutions up to @math ) on the MNIST dataset. Compared to a PixelCNN++ baseline, Spatial PixelCNN quantitatively and qualitatively achieves similar performance on the MNIST dataset.
Pixel Recurrent Neural Networks @cite_3 (PixelRNN), are a class of powerful generative model. PixelRNN is an explicit generative model which can be trained to directly maximize the likelihood of the training data. Here, the likelihood @math of each 2-D image @math is decomposed via chain rule into:
@cite_3
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Modeling the distribution of natural images is a landmark problem in unsupervised learning. This task requires an image model that is at once expressive, tractable and scalable. We present a deep neural network that sequentially predicts the pixels in an image along the two spatial dimensions. Our method models the discrete probability of the raw pixel values and encodes the complete set of dependencies in the image. Architectural novelties include fast two-dimensional recurrent layers and an effective use of residual connections in deep recurrent networks. We achieve log-likelihood scores on natural images that are considerably better than the previous state of the art. Our main results also provide benchmarks on the diverse ImageNet dataset. Samples generated from the model appear crisp, varied and globally coherent.