# MaCow: Masked Convolutional Generative Flow

arXiv: https://arxiv.org/abs/1902.04208 · HTML: https://mlsanity.com/paper/1902.04208/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2019.

## Built on by (most cited first, 30 of 32)

- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [ArtFlow: Unbiased Image Style Transfer via Reversible Neural Flows](https://mlsanity.com/paper/2103.16877/) (2021)
- [Densely connected normalizing flows](https://mlsanity.com/paper/2106.04627/) (2021)
- [iPOKE: Poking a Still Image for Controlled Stochastic Video Synthesis](https://mlsanity.com/paper/2107.02790/) (2021)
- [Resampling Base Distributions of Normalizing Flows](https://mlsanity.com/paper/2110.15828/) (2021)
- [Efficient-VDVAE: Less is more](https://mlsanity.com/paper/2203.13751/) (2022)
- [Maximum Entropy Reinforcement Learning via Energy-Based Normalizing Flow](https://mlsanity.com/paper/2405.13629/) (2024)
- [ManiFPT: Defining and Analyzing Fingerprints of Generative Models](https://mlsanity.com/paper/2402.10401/) (2024)
- [Personalized Public Policy Analysis in Social Sciences using Causal-Graphical Normalizing Flows](https://mlsanity.com/paper/2202.03281/) (2022)
- [ButterflyFlow: Building Invertible Layers with Butterfly Matrices](https://mlsanity.com/paper/2209.13774/) (2022)
- [PassFlow: Guessing Passwords with Generative Flows](https://mlsanity.com/paper/2105.06165/) (2021)
- [Riemannian-Geometric Fingerprints of Generative Models](https://mlsanity.com/paper/2506.22802/) (2025)
- [Training Energy-Based Normalizing Flow with Score-Matching Objectives](https://mlsanity.com/paper/2305.15267/) (2023)
- [Entropy-Informed Weighting Channel Normalizing Flow for Deep Generative Models](https://mlsanity.com/paper/2407.04958/) (2024)
- [Multi-Resolution Continuous Normalizing Flows](https://mlsanity.com/paper/2106.08462/) (2021)
- [Robust Vector Quantized-Variational Autoencoder](https://mlsanity.com/paper/2202.01987/) (2022)
- [A Non-negative VAE:the Generalized Gamma Belief Network](https://mlsanity.com/paper/2408.03388/) (2024)
- [Flow-based Spatio-Temporal Structured Prediction of Motion Dynamics](https://mlsanity.com/paper/2104.04391/) (2021)
- [FInC Flow: Fast and Invertible k × k Convolutions for Normalizing Flows](https://mlsanity.com/paper/2301.09266/) (2023)
- [GMConv: Modulating Effective Receptive Fields for Convolutional Kernels](https://mlsanity.com/paper/2302.04544/) (2023)
- [PixelPyramids: Exact Inference Models from Lossless Image Pyramids](https://mlsanity.com/paper/2110.08787/) (2021)
- [ELF: Exact-Lipschitz Based Universal Density Approximator Flow](https://mlsanity.com/paper/2112.06997/) (2021)
- [3D GANs and Latent Space: A comprehensive survey](https://mlsanity.com/paper/2304.03932/) (2023)
- [VeriFlow: Modeling Distributions for Neural Network Verification](https://mlsanity.com/paper/2406.14265/) (2024)
- [Sinusoidal Flow: A Fast Invertible Autoregressive Flow](https://mlsanity.com/paper/2110.13344/) (2021)
- [Learning Robust Representations Of Generative Models Using Set-Based Artificial Fingerprints](https://mlsanity.com/paper/2206.02067/) (2022)
- [Invertible Convolution with Symmetric Paddings](https://mlsanity.com/paper/2303.17361/) (2023)
- [Realistic Restorer: artifact-free flow restorer(AF2R) for MRI motion artifact removal](https://mlsanity.com/paper/2306.10689/) (2023)
- [MixerFlow: MLP-Mixer meets Normalising Flows](https://mlsanity.com/paper/2310.16777/) (2023)
- [Parallel Backpropagation for Inverse of a Convolution with Application to Normalizing Flows](https://mlsanity.com/paper/2410.14634/) (2024)

## Abstract (arXiv)

Flow-based generative models, conceptually attractive due to tractability of both the exact log-likelihood computation and latent-variable inference, and efficiency of both training and sampling, has led to a number of impressive empirical successes and spawned many advanced variants and theoretical investigations. Despite their computational efficiency, the density estimation performance of flow-based generative models significantly falls behind those of state-of-the-art autoregressive models. In this work, we introduce masked convolutional generative flow (MaCow), a simple yet effective architecture of generative flow using masked convolution. By restricting the local connectivity in a small kernel, MaCow enjoys the properties of fast and stable training, and efficient sampling, while achieving significant improvements over Glow for density estimation on standard image benchmarks, considerably narrowing the gap to autoregressive models.