Bridging Diffusion Guidance and Anderson Acceleration via Hopfield Dynamics

2026-03-02

AI Summary

This work addresses the high inference cost and incompatibility with distillation or single-step generation inherent in Classifier-Free Guidance for diffusion models, as well as the lack of theoretical grounding in existing attention-based extrapolation methods. The authors establish a novel connection by modeling attention dynamics as fixed-point iterations in modern Hopfield networks, revealing that attention extrapolation is a special case of Anderson acceleration. Building on this insight, they propose Geometry-Aware Guidance (GAG), a plug-and-play acceleration mechanism grounded in directional decomposition and weak contractivity analysis. GAG ensures stable and efficient inference while seamlessly integrating into existing diffusion frameworks, significantly improving generation quality without sacrificing computational efficiency.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

Classifier-Free Guidance (CFG) has significantly enhanced the generative quality of diffusion models by extrapolating between conditional and unconditional outputs. However, its high inference cost and limited applicability to distilled or single-step models have shifted research focus toward attention-space extrapolation. While these methods offer computational efficiency, their theoretical underpinnings remain elusive. In this work, we establish a foundational framework for attention-space extrapolation by modeling attention dynamics as fixed-point iterations within Modern Hopfield Networks. We demonstrate that the extrapolation effect in attention space constitutes a special case of Anderson Acceleration applied to these dynamics. Building on this insight and the weak contraction property, we propose Geometry Aware Attention Guidance (GAG). By decomposing attention updates into parallel and orthogonal components relative to the guidance direction, GAG stabilizes the acceleration process and maximizes guidance efficiency. Our plug-and-play method seamlessly integrates with existing frameworks while significantly improving generation quality.

Problem

• Classifier-Free Guidance
• diffusion models
• attention-space extrapolation
• Anderson Acceleration
• Hopfield Networks

Innovation

• Hopfield Dynamics
• Anderson Acceleration
• Attention-Space Extrapolation
• Classifier-Free Guidance
• Geometry Aware Attention Guidance