Emerging Convolutions for Generative Normalizing Flows

TL;DR

This paper introduces invertible d x d convolutions for generative normalizing flows, enhancing their flexibility and performance in image generation tasks across various datasets.

Contribution

It generalizes 1 x 1 convolutions to invertible d x d convolutions using two novel methods, improving generative flow models.

Findings

Improved image generation quality on galaxy images, CIFAR10, and ImageNet.

Enhanced model flexibility with d x d convolutions.

Significant performance gains demonstrated in experiments.

Abstract

Generative flows are attractive because they admit exact likelihood optimization and efficient image synthesis. Recently, Kingma & Dhariwal (2018) demonstrated with Glow that generative flows are capable of generating high quality images. We generalize the 1 x 1 convolutions proposed in Glow to invertible d x d convolutions, which are more flexible since they operate on both channel and spatial axes. We propose two methods to produce invertible convolutions that have receptive fields identical to standard convolutions: Emerging convolutions are obtained by chaining specific autoregressive convolutions, and periodic convolutions are decoupled in the frequency domain. Our experiments show that the flexibility of d x d convolutions significantly improves the performance of generative flow models on galaxy images, CIFAR10 and ImageNet.