# Geometry-Aware Attention Guidance for Diffusion Models via Modern Hopfield Dynamics

arXiv: https://arxiv.org/abs/2603.02531 · HTML: https://mlsanity.com/paper/2603.02531/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 42 of its 63 references that are in the map.
- First posted on arXiv 3 Mar 2026.

## Placed in

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

## Builds on (most cited first, 30 of 42)

- [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)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [CogVideoX: Text-to-Video Diffusion Models with An Expert Transformer](https://mlsanity.com/paper/2408.06072/) (2024)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Qwen-Image Technical Report](https://mlsanity.com/paper/2508.02324/) (2025)
- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [GenEval: An Object-Focused Framework for Evaluating Text-to-Image Alignment](https://mlsanity.com/paper/2310.11513/) (2023)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [VideoCrafter2: Overcoming Data Limitations for High-Quality Video Diffusion Models](https://mlsanity.com/paper/2401.09047/) (2024)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification](https://mlsanity.com/paper/1602.02068/) (2016)
- [SANA: Efficient High-Resolution Image Synthesis with Linear Diffusion Transformers](https://mlsanity.com/paper/2410.10629/) (2024)
- [SDXL-Lightning: Progressive Adversarial Diffusion Distillation](https://mlsanity.com/paper/2402.13929/) (2024)
- [Dense Associative Memory for Pattern Recognition](https://mlsanity.com/paper/1606.01164/) (2016)
- [Sparse Sequence-to-Sequence Models](https://mlsanity.com/paper/1905.05702/) (2019)
- [Hyper-SD: Trajectory Segmented Consistency Model for Efficient Image Synthesis](https://mlsanity.com/paper/2404.13686/) (2024)
- [Eliminating Oversaturation and Artifacts of High Guidance Scales in Diffusion Models](https://mlsanity.com/paper/2410.02416/) (2024)

## Abstract (arXiv)

Classifier-Free Guidance (CFG) improves sample quality in diffusion models, but its dual-pass inference and reliance on null-condition training limit its use in few-step regimes. Attention-space guidance has emerged as a complementary paradigm that addresses this gap, yet why prior sparse-vs-dense attention guidance works remains elusive. We address this by analyzing attention extrapolation through Modern Hopfield dynamics, proving two directional properties of the sparse-dense discrepancy under shared conditioning that together certify it as a directionally consistent acceleration signal. Building on this, we propose Geometry-Aware Attention Guidance (GAG), a training-free, plug-and-play extrapolation rule that decomposes the discrepancy into parallel and orthogonal components relative to the retrieval direction, amplifying the convergence-aligned component while suppressing off-manifold noise; stability follows from a weak contraction property. We further provide an interpretation of this extrapolation as first-order Anderson Acceleration in attention space, offering a unified perspective on attention extrapolation methods. GAG is a universal method that generalizes across architectures (UNet, MMDiT) and sampling regimes (multi-step, few-step), consistently improving generation quality on diverse backbones, including FLUX.1, the recent FLUX.2, and Qwen-Image, with minimal computational overhead.