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 to achieve 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.

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 to achieve 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.

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.

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 to achieve 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.