# Autoregressive Quantile Networks for Generative Modeling

arXiv: https://arxiv.org/abs/1806.05575 · HTML: https://mlsanity.com/paper/1806.05575/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2018.

## Built on by (most cited first, 30 of 31)

- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Generative Modeling with Optimal Transport Maps](https://mlsanity.com/paper/2110.02999/) (2021)
- [Densely connected normalizing flows](https://mlsanity.com/paper/2106.04627/) (2021)
- [A Tale of Two Flows: Cooperative Learning of Langevin Flow and Normalizing Flow Toward Energy-Based Model](https://mlsanity.com/paper/2205.06924/) (2022)
- [Distributional GFlowNets with Quantile Flows](https://mlsanity.com/paper/2302.05793/) (2023)
- [Diffusion Probabilistic Fields](https://mlsanity.com/paper/2303.00165/) (2023)
- [Generative AI for End-to-End Limit Order Book Modelling: A Token-Level Autoregressive Generative Model of Message Flow Using a Deep State Space Network](https://mlsanity.com/paper/2309.00638/) (2023)
- [Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihood](https://mlsanity.com/paper/2309.05153/) (2023)
- [Improved Autoregressive Modeling with Distribution Smoothing](https://mlsanity.com/paper/2103.15089/) (2021)
- [Probabilistic Time Series Forecasting with Implicit Quantile Networks](https://mlsanity.com/paper/2107.03743/) (2021)
- [Relational Conformal Prediction for Correlated Time Series](https://mlsanity.com/paper/2502.09443/) (2025)
- [Inference and Sampling for Archimax Copulas](https://mlsanity.com/paper/2205.14025/) (2022)
- [DiffGAR: Model-Agnostic Restoration from Generative Artifacts Using Image-to-Image Diffusion Models](https://mlsanity.com/paper/2210.08573/) (2022)
- [Entropy-Informed Weighting Channel Normalizing Flow for Deep Generative Models](https://mlsanity.com/paper/2407.04958/) (2024)
- [Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamics](https://mlsanity.com/paper/2510.12311/) (2025)
- [Funnels: Exact maximum likelihood with dimensionality reduction](https://mlsanity.com/paper/2112.08069/) (2021)
- [Learning to Simulate: Generative Metamodeling via Quantile Regression](https://mlsanity.com/paper/2311.17797/) (2023)
- [CoopInit: Initializing Generative Adversarial Networks via Cooperative Learning](https://mlsanity.com/paper/2303.11649/) (2023)
- [Survey on Visual Signal Coding and Processing with Generative Models: Technologies, Standards and Optimization](https://mlsanity.com/paper/2405.14221/) (2024)
- [Deep Generative Quantile Bayes](https://mlsanity.com/paper/2410.08378/) (2024)
- [Generative Modeling: A Review](https://mlsanity.com/paper/2501.05458/) (2024)
- [Adapting deep generative approaches for getting synthetic data with realistic marginal distributions](https://mlsanity.com/paper/2105.06907/) (2021)
- [Implicit Quantile Neural Networks for Jet Simulation and Correction](https://mlsanity.com/paper/2111.11415/) (2021)
- [Learning Stationary Markov Processes with Contrastive Adjustment](https://mlsanity.com/paper/2303.05497/) (2023)
- [Deep Generative Methods for Producing Forecast Trajectories in Power Systems](https://mlsanity.com/paper/2309.15137/) (2023)
- [Combining propensity score methods with variational autoencoders for generating synthetic data in presence of latent sub-groups](https://mlsanity.com/paper/2312.07781/) (2023)
- [Variational Potential Flow: A Novel Probabilistic Framework for Energy-Based Generative Modelling](https://mlsanity.com/paper/2407.15238/) (2024)
- [A Data-driven Dynamic Temporal Correlation Modeling Framework for Renewable Energy Scenario Generation](https://mlsanity.com/paper/2501.14233/) (2025)
- [Discrete Markov Bridge](https://mlsanity.com/paper/2505.19752/) (2025)
- [QUTCC: Quantile Uncertainty Training and Conformal Calibration for Imaging Inverse Problems](https://mlsanity.com/paper/2507.14760/) (2025)

## Abstract (arXiv)

We introduce autoregressive implicit quantile networks (AIQN), a fundamentally different approach to generative modeling than those commonly used, that implicitly captures the distribution using quantile regression. AIQN is able to achieve superior perceptual quality and improvements in evaluation metrics, without incurring a loss of sample diversity. The method can be applied to many existing models and architectures. In this work we extend the PixelCNN model with AIQN and demonstrate results on CIFAR-10 and ImageNet using Inception score, FID, non-cherry-picked samples, and inpainting results. We consistently observe that AIQN yields a highly stable algorithm that improves perceptual quality while maintaining a highly diverse distribution.