# Fast Flow Reconstruction via Robust Invertible nxn Convolution

## TL;DR

This paper introduces an invertible n x n convolution that enhances flow-based generative models by increasing flexibility, reducing parameters, and improving performance on multiple datasets.

## Contribution

It proposes a novel invertible n x n convolution that overcomes the limitations of 1 x 1 convolutions in flow models, with fewer parameters and better results.

## Key findings

- Improved generative model performance on CIFAR-10, ImageNet, Celeb-HQ.
- Fewer parameters than standard convolutions.
- Enhanced flexibility over invertible 1 x 1 convolutions.

## Abstract

Flow-based generative models have recently become one of the most efficient approaches to model data generation. Indeed, they are constructed with a sequence of invertible and tractable transformations. Glow first introduced a simple type of generative flow using an invertible $1 \times 1$ convolution. However, the $1 \times 1$ convolution suffers from limited flexibility compared to the standard convolutions. In this paper, we propose a novel invertible $n \times n$ convolution approach that overcomes the limitations of the invertible $1 \times 1$ convolution. In addition, our proposed network is not only tractable and invertible but also uses fewer parameters than standard convolutions. The experiments on CIFAR-10, ImageNet and Celeb-HQ datasets, have shown that our invertible $n \times n$ convolution helps to improve the performance of generative models significantly.