Normalizing Flows are Capable Generative Models
Authors: name: Shuangfei Zhai, name: Ruixiang Zhang, name: Preetum Nakkiran, name: David Berthelot, name: Jiatao Gu, name: Huangjie Zheng, name: Tianrong Chen, name: Miguel Angel Bautista, name: Navdeep Jaitly, name: Josh Susskind

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.