Discretized Approximate Ancestral Sampling

The Fourier Basis Density Model (FBM) was recently introduced as a flexible probability model for band-limited distributions, i.e. ones which are smooth in the sense of having a characteristic function with limited support around the origin. Its density and cumulative distribution functions can be efficiently evaluated and trained with stochastic optimization methods, which makes the model suitable for deep learning applications. However, the model lacked support for sampling. Here, we introduce a method inspired by discretization--interpolation methods common in Digital Signal Processing, which directly take advantage of the band-limited property. We review mathematical properties of the FBM, and prove quality bounds of the sampled distribution in terms of the total variation (TV) and Wasserstein--1 divergences from the model. These bounds can be used to inform the choice of hyperparameters to reach any desired sample quality. We discuss these results in comparison to a variety of other sampling techniques, highlighting tradeoffs between computational complexity and sampling quality.

Good, Cheap, and Fast: Overfitted Image Compression with Wasserstein Distortion

Inspired by the success of generative image models, recent work on learned image compression increasingly focuses on better probabilistic models of the natural image distribution, leading to excellent image quality. This, however, comes at the expense of a computational complexity that is several orders of magnitude higher than today's commercial codecs, and thus prohibitive for most practical applications. With this paper, we demonstrate that by focusing on modeling visual perception rather than the data distribution, we can achieve a very good trade-off between visual quality and bit rate similar to "generative" compression models such as HiFiC, while requiring less than 1% of the multiply-accumulate operations (MACs) for decompression. We do this by optimizing C3, an overfitted image codec, for Wasserstein Distortion (WD), and evaluating the image reconstructions with a human rater study. The study also reveals that WD outperforms other perceptual quality metrics such as LPIPS, DISTS, and MS-SSIM, both as an optimization objective and as a predictor of human ratings, achieving over 94% Pearson correlation with Elo scores.