# Fast Flow Reconstruction via Robust Invertible nxn Convolution

Source: [Fast Flow Reconstruction via Robust Invertible nxn Convolution](<https://www.sota2.com/research/paper/68fa6d351e209131cea386a1>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:56:54.756Z

Authors: Thanh-Dat Truong, Khoa Luu, Chi Nhan Duong, Ngan Le, Minh-Triet Tran

Published: 2019-05-24T11:58:05.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1905.10170>)

[PDF](<https://arxiv.org/pdf/1905.10170.pdf>)