# Accelerate TarFlow Sampling with GS-Jacobi Iteration

arXiv: https://arxiv.org/abs/2505.12849 · HTML: https://mlsanity.com/paper/2505.12849/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 35 references that are in the map.
- First posted on arXiv 19 May 2025.

## Builds on (most cited first, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [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)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [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)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [Parallel WaveNet: Fast High-Fidelity Speech Synthesis](https://mlsanity.com/paper/1711.10433/) (2017)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [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)
- [Block Neural Autoregressive Flow](https://mlsanity.com/paper/1904.04676/) (2019)
- [Conditional Density Estimation with Bayesian Normalising Flows](https://mlsanity.com/paper/1802.04908/) (2018)
- [Accelerating Feedforward Computation via Parallel Nonlinear Equation Solving](https://mlsanity.com/paper/2002.03629/) (2020)
- [Latent Variable Modelling with Hyperbolic Normalizing Flows](https://mlsanity.com/paper/2002.06336/) (2020)
- [Composing Normalizing Flows for Inverse Problems](https://mlsanity.com/paper/2002.11743/) (2020)
- [Densely connected normalizing flows](https://mlsanity.com/paper/2106.04627/) (2021)
- [MintNet: Building Invertible Neural Networks with Masked Convolutions](https://mlsanity.com/paper/1907.07945/) (2019)
- [Learning Generative Models using Denoising Density Estimators](https://mlsanity.com/paper/2001.02728/) (2020)
- [Transformer Neural Autoregressive Flows](https://mlsanity.com/paper/2401.01855/) (2024)
- [Parallel Complexity of Forward and Backward Propagation](https://mlsanity.com/paper/1712.06577/) (2017)

## Built on by (most cited first, 2 of 2)

- [STARFlow-V: End-to-End Video Generative Modeling with Normalizing Flows](https://mlsanity.com/paper/2511.20462/) (2025)
- [The Coupling Within: Flow Matching via Distilled Normalizing Flows](https://mlsanity.com/paper/2603.09014/) (2026)

## Abstract (arXiv)

Image generation models have achieved widespread applications. As an instance, the TarFlow model combines the transformer architecture with Normalizing Flow models, achieving state-of-the-art results on multiple benchmarks. However, due to the causal form of attention requiring sequential computation, TarFlow's sampling process is extremely slow. In this paper, we demonstrate that through a series of optimization strategies, TarFlow sampling can be greatly accelerated by using the Gauss-Seidel-Jacobi (abbreviated as GS-Jacobi) iteration method. Specifically, we find that blocks in the TarFlow model have varying importance: a small number of blocks play a major role in image generation tasks, while other blocks contribute relatively little; some blocks are sensitive to initial values and prone to numerical overflow, while others are relatively robust. Based on these two characteristics, we propose the Convergence Ranking Metric (CRM) and the Initial Guessing Metric (IGM): CRM is used to identify whether a TarFlow block is "simple" (converges in few iterations) or "tough" (requires more iterations); IGM is used to evaluate whether the initial value of the iteration is good. Experiments on four TarFlow models demonstrate that GS-Jacobi sampling can significantly enhance sampling efficiency while maintaining the quality of generated images (measured by FID), achieving speed-ups of 4.53x in Img128cond, 5.32x in AFHQ, 2.96x in Img64uncond, and 2.51x in Img64cond without degrading FID scores or sample quality. Code and checkpoints are accessible on https://github.com/encoreus/GS-Jacobi_for_TarFlow