Review for NeurIPS paper: Wavelet Flow: Fast Training of High Resolution Normalizing Flows

Summary and Contributions: This paper introduces a hierarchical structure for normalizing flows for density estimation and data generation based on wavelet transforms, allowing for a natural factorization of the data distribution based on different resolutions of the data. For density estimation, each image is fed into a sequence of wavelet transforms. Each wavelet transform takes an image and outputs a lower resolution image (obtained by a low-pass filter) and a tensor of detail coefficients (obtained by a high-pass filter). Repeatedly applying wavelet transforms to the output images leads to a set of detail coefficient tensors for each scale and a final 1x1x3 "image" representing the average intensity per channel. The original representation can be recovered from this representation with a sequence of inverse wavelet transforms.