Normalizing flows are a class of probabilistic generative models which allow for both fast density computation and efficient sampling and are effective at modelling complex distributions like images. A drawback among current methods is their significant training cost, sometimes requiring months of GPU training time toachieve state-of-the-art results. This paper introduces Wavelet Flow, a multi-scale, normalizing flow architecture based on wavelets. A Wavelet Flow has an explicit representation of signal scale that inherently includes models of lower resolution signals and conditional generation of higher resolution signals, i.e., super resolution. A major advantage of Wavelet Flow is the ability to construct generative models for high resolution data (e.g., 1024×1024 images) that are impractical with previous models. Furthermore, Wavelet Flow is competitive with previous normalizing flows in terms of bits per dimension on standard (low resolution) benchmarks while being up to 15× faster to train.

Recently, convolutional networks (convnets) have proven useful for predicting optical flow. Much of this success is predicated on the availability of large datasets that require expensive and involved data acquisition and laborious labeling. To bypass these challenges, we propose an unsupervised approach (i.e., without leveraging groundtruth flow) to train a convnet end-to-end for predicting optical flow between two images. We use a loss function that combines a data term that measures photometric constancy over time with a spatial term that models the expected variation of flow across the image. Together these losses form a proxy measure for losses based on the groundtruth flow. Empirically, we show that a strong convnet baseline trained with the proposed unsupervised approach outperforms the same network trained with supervision on the KITTI dataset.