FInC Flow: Fast and Invertible k × k Convolutions for Normalizing Flows

Invertible convolutions have been an essential element for building expressive normalizing flow-based generative models since their introduction in Glow. Several attempts have been made to design invertible k × k convolutions that are efficient in training and sampling passes. Though these attempts have improved the expressivity and sampling efficiency, they severely lagged behind Glow which used only 1 × 1 convolutions in terms of sampling time. Also, many of the approaches mask a large number of parameters of the underlying convolution, resulting in lower expressivity on a fixed run-time budget. We propose a k × k convolutional layer and Deep Normalizing Flow architecture which (i) has a fast parallel inversion algorithm with running time O(n k^2) (n is height and width of the input image and k is kernel size), (ii) masks the minimal amount of learnable parameters in a layer, and (iii) gives better forward pass and sampling times comparable to other k × k convolution-based models on real-world benchmarks.

In Proceedings of the 18th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2023) - Volume 5: VISAPP, pp. 338–348