# Normalizing Flows with Multi-Scale Autoregressive Priors Source: [Normalizing Flows with Multi-Scale Autoregressive Priors]() Collection index: [llms.txt]() Data updated: 2025-10-25T22:11:14.110Z Authors: Shweta Mahajan, Apratim Bhattacharyya, Mario Fritz, Bernt Schiele, Stefan Roth Published: 2020-04-08T09:07:11.000Z ## Abstract 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. ## 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. - [Image Generation on CIFAR-10 (test)](): Image Generation; CIFAR-10 (test); FID: 40.5. - [Image Generation on MNIST](): Image Generation; MNIST; FID: not recorded. ## Original sources and implementation [Original paper]() [PDF]()