Emerging Convolutions for Generative Normalizing Flows
This work addresses the need for more flexible and efficient generative models for image synthesis, though it is incremental as it builds on existing flow-based methods like Glow.
The paper tackles the problem of improving generative normalizing flows by generalizing 1x1 convolutions to invertible d x d convolutions, which operate on both channel and spatial axes, resulting in significant performance gains on datasets like galaxy images, CIFAR10, and ImageNet.
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.