# Accelerating Inference of Discrete Autoregressive Normalizing Flows by Selective Jacobi Decoding

arXiv: https://arxiv.org/abs/2505.24791 · HTML: https://mlsanity.com/paper/2505.24791/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 34 references that are in the map.
- First posted on arXiv 30 May 2025.

## Builds on (most cited first, 25 of 25)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [fairseq: A Fast, Extensible Toolkit for Sequence Modeling](https://mlsanity.com/paper/1904.01038/) (2019)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Exploring CLIP for Assessing the Look and Feel of Images](https://mlsanity.com/paper/2207.12396/) (2022)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [GENIE: Higher-Order Denoising Diffusion Solvers](https://mlsanity.com/paper/2210.05475/) (2022)
- [Accelerating Transformer Inference for Translation via Parallel Decoding](https://mlsanity.com/paper/2305.10427/) (2023)
- [Normalizing Flows are Capable Generative Models](https://mlsanity.com/paper/2412.06329/) (2024)
- [CLLMs: Consistency Large Language Models](https://mlsanity.com/paper/2403.00835/) (2024)
- [Accelerating Auto-regressive Text-to-Image Generation with Training-free Speculative Jacobi Decoding](https://mlsanity.com/paper/2410.01699/) (2024)
- [Accelerating Feedforward Computation via Parallel Nonlinear Equation Solving](https://mlsanity.com/paper/2002.03629/) (2020)
- [Compressing GANs using Knowledge Distillation](https://mlsanity.com/paper/1902.00159/) (2019)
- [Improving the Speed and Quality of GAN by Adversarial Training](https://mlsanity.com/paper/2008.03364/) (2020)
- [Quantization of Generative Adversarial Networks for Efficient Inference: a Methodological Study](https://mlsanity.com/paper/2108.13996/) (2021)
- [CoroNetGAN: Controlled Pruning of GANs via Hypernetworks](https://mlsanity.com/paper/2403.08261/) (2024)
- [Nickel and Diming Your GAN: A Dual-Method Approach to Enhancing GAN Efficiency via Knowledge Distillation](https://mlsanity.com/paper/2405.11614/) (2024)

## Built on by (most cited first, 1 of 1)

- [STARFlow-V: End-to-End Video Generative Modeling with Normalizing Flows](https://mlsanity.com/paper/2511.20462/) (2025)

## Abstract (arXiv)

Discrete normalizing flows are promising generative models with advantages such as analytical log-likelihood computation and end-to-end training. However, the architectural constraints to ensure invertibility and tractable Jacobian computation limit their expressive power and practical usability. Recent advancements utilize autoregressive modeling, significantly enhancing expressive power and generation quality. Nevertheless, such sequential modeling inherently restricts parallel computation during inference, leading to slow generation that impedes practical deployment. In this paper, we first identify that strict sequential dependency in inference is unnecessary to generate high-quality samples. We observe that sub-variables in sequential modeling can also be approximated without strictly conditioning on all preceding sub-variables. Moreover, the models tend to exhibit low dependency redundancy in the initial layer and higher redundancy in subsequent layers. Leveraging these observations, we propose to selectively use Jacobi decoding strategy that accelerates its autoregressive inference through parallel iterative optimization. Theoretical analyses demonstrate the method's superlinear convergence rate and guarantee that the number of iterations required is no greater than the original sequential approach. Empirical evaluations across multiple datasets validate the generality and effectiveness of our acceleration technique, achieving up to 4.7 times faster inference on modern normalizing flow models while preserving generation quality.