# Normalizing Flows with Multi-Scale Autoregressive Priors

arXiv: https://arxiv.org/abs/2004.03891 · HTML: https://mlsanity.com/paper/2004.03891/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2020.

## Built on by (most cited first, 11 of 11)

- [Make-A-Story: Visual Memory Conditioned Consistent Story Generation](https://mlsanity.com/paper/2211.13319/) (2022)
- [Densely connected normalizing flows](https://mlsanity.com/paper/2106.04627/) (2021)
- [Resampling Base Distributions of Normalizing Flows](https://mlsanity.com/paper/2110.15828/) (2021)
- [Prompting Hard or Hardly Prompting: Prompt Inversion for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2312.12416/) (2023)
- [Generative Flows with Invertible Attentions](https://mlsanity.com/paper/2106.03959/) (2021)
- [Jet: A Modern Transformer-Based Normalizing Flow](https://mlsanity.com/paper/2412.15129/) (2024)
- [Entropy-Informed Weighting Channel Normalizing Flow for Deep Generative Models](https://mlsanity.com/paper/2407.04958/) (2024)
- [AltUB: Alternating Training Method to Update Base Distribution of Normalizing Flow for Anomaly Detection](https://mlsanity.com/paper/2210.14913/) (2022)
- [HybridFlow: Quantification of Aleatoric and Epistemic Uncertainty with a Single Hybrid Model](https://mlsanity.com/paper/2510.05054/) (2025)
- [PixelPyramids: Exact Inference Models from Lossless Image Pyramids](https://mlsanity.com/paper/2110.08787/) (2021)
- [Normalizing Flow with Variational Latent Representation](https://mlsanity.com/paper/2211.11638/) (2022)

## Abstract (arXiv)

Flow-based generative models are an important class of exact inference models that admit efficient inference and sampling for image synthesis. Owing to the efficiency constraints on the design of the flow layers, e.g. split coupling flow layers in which approximately half the pixels do not undergo further transformations, they have limited expressiveness for modeling long-range data dependencies compared to autoregressive models that rely on conditional pixel-wise generation. In this work, we improve the representational power of flow-based models by introducing channel-wise dependencies in their latent space through multi-scale autoregressive priors (mAR). Our mAR prior for models with split coupling flow layers (mAR-SCF) can better capture dependencies in complex multimodal data. The resulting model achieves state-of-the-art density estimation results on MNIST, CIFAR-10, and ImageNet. Furthermore, we show that mAR-SCF allows for improved image generation quality, with gains in FID and Inception scores compared to state-of-the-art flow-based models.