Normalizing Flows are Capable Generative Models

TL;DR

This paper introduces TarFlow, a Transformer-based normalizing flow architecture that achieves state-of-the-art likelihood estimation and high-quality image generation, rivaling diffusion models.

Contribution

The paper presents TarFlow, a scalable Transformer-based normalizing flow model with techniques to enhance sample quality, setting new benchmarks in likelihood estimation and image generation.

Findings

TarFlow achieves state-of-the-art likelihood estimation on images.

TarFlow generates high-quality, diverse images comparable to diffusion models.

The proposed techniques significantly improve sample quality in normalizing flows.

Abstract

Normalizing Flows (NFs) are likelihood-based models for continuous inputs. They have demonstrated promising results on both density estimation and generative modeling tasks, but have received relatively little attention in recent years. In this work, we demonstrate that NFs are more powerful than previously believed. We present TarFlow: a simple and scalable architecture that enables highly performant NF models. TarFlow can be thought of as a Transformer-based variant of Masked Autoregressive Flows (MAFs): it consists of a stack of autoregressive Transformer blocks on image patches, alternating the autoregression direction between layers. TarFlow is straightforward to train end-to-end, and capable of directly modeling and generating pixels. We also propose three key techniques to improve sample quality: Gaussian noise augmentation during training, a post training denoising procedure, and an effective guidance method for both class-conditional and unconditional settings. Putting these together, TarFlow sets new state-of-the-art results on likelihood estimation for images, beating the previous best methods by a large margin, and generates samples with quality and diversity comparable to diffusion models, for the first time with a stand-alone NF model. We make our code available at https://github.com/apple/ml-tarflow.