# HOFAR: High-Order Augmentation of Flow Autoregressive Transformers

arXiv: https://arxiv.org/abs/2503.08032 · HTML: https://mlsanity.com/paper/2503.08032/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 51 of its 55 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 51)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Make-A-Video: Text-to-Video Generation without Text-Video Data](https://mlsanity.com/paper/2209.14792/) (2022)
- [Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Prediction](https://mlsanity.com/paper/2404.02905/) (2024)
- [Autoregressive Image Generation without Vector Quantization](https://mlsanity.com/paper/2406.11838/) (2024)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Simple diffusion: End-to-end diffusion for high resolution images](https://mlsanity.com/paper/2301.11093/) (2023)
- [Pyramidal Flow Matching for Efficient Video Generative Modeling](https://mlsanity.com/paper/2410.05954/) (2024)
- [MagicAnimate: Temporally Consistent Human Image Animation using Diffusion Model](https://mlsanity.com/paper/2311.16498/) (2023)
- [How to train your neural ODE: the world of Jacobian and kinetic regularization](https://mlsanity.com/paper/2002.02798/) (2020)
- [4Diffusion: Multi-view Video Diffusion Model for 4D Generation](https://mlsanity.com/paper/2405.20674/) (2024)
- [Diffusion4D: Fast Spatial-temporal Consistent 4D Generation via Video Diffusion Models](https://mlsanity.com/paper/2405.16645/) (2024)
- [HumanNorm: Learning Normal Diffusion Model for High-quality and Realistic 3D Human Generation](https://mlsanity.com/paper/2310.01406/) (2023)
- [Learning Differential Equations that are Easy to Solve](https://mlsanity.com/paper/2007.04504/) (2020)
- [FlowAR: Scale-wise Autoregressive Image Generation Meets Flow Matching](https://mlsanity.com/paper/2412.15205/) (2024)
- [Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion](https://mlsanity.com/paper/2312.00852/) (2023)
- [VideoGen: A Reference-Guided Latent Diffusion Approach for High Definition Text-to-Video Generation](https://mlsanity.com/paper/2309.00398/) (2023)
- [Video Interpolation with Diffusion Models](https://mlsanity.com/paper/2404.01203/) (2024)
- [On Exact Inversion of DPM-Solvers](https://mlsanity.com/paper/2311.18387/) (2023)
- [NoiseCLR: A Contrastive Learning Approach for Unsupervised Discovery of Interpretable Directions in Diffusion Models](https://mlsanity.com/paper/2312.05390/) (2023)
- [TokenCompose: Text-to-Image Diffusion with Token-level Supervision](https://mlsanity.com/paper/2312.03626/) (2023)
- [LazyDiT: Lazy Learning for the Acceleration of Diffusion Transformers](https://mlsanity.com/paper/2412.12444/) (2024)
- [DiffPortrait3D: Controllable Diffusion for Zero-Shot Portrait View Synthesis](https://mlsanity.com/paper/2312.13016/) (2023)
- [Unraveling the Smoothness Properties of Diffusion Models: A Gaussian Mixture Perspective](https://mlsanity.com/paper/2405.16418/) (2024)

## Built on by (most cited first, 4 of 4)

- [T2VWorldBench: A Benchmark for Evaluating World Knowledge in Text-to-Video Generation](https://mlsanity.com/paper/2507.18107/) (2025)
- [T2VTextBench: A Human Evaluation Benchmark for Textual Control in Video Generation Models](https://mlsanity.com/paper/2505.04946/) (2025)
- [Towards High-Order Mean Flow Generative Models: Feasibility, Expressivity, and Provably Efficient Criteria](https://mlsanity.com/paper/2508.07102/) (2025)
- [Fundamental Limits of Crystalline Equivariant Graph Neural Networks: A Circuit Complexity Perspective](https://mlsanity.com/paper/2510.05494/) (2025)

## Abstract (arXiv)

Flow Matching and Transformer architectures have demonstrated remarkable performance in image generation tasks, with recent work FlowAR [Ren et al., 2024] synergistically integrating both paradigms to advance synthesis fidelity. However, current FlowAR implementations remain constrained by first-order trajectory modeling during the generation process. This paper introduces a novel framework that systematically enhances flow autoregressive transformers through high-order supervision. We provide theoretical analysis and empirical evaluation showing that our High-Order FlowAR (HOFAR) demonstrates measurable improvements in generation quality compared to baseline models. The proposed approach advances the understanding of flow-based autoregressive modeling by introducing a systematic framework for analyzing trajectory dynamics through high-order expansion.