Let Attention Flow: Energy-Dissipating Guidance for Diffusion Models

Diffusion models achieve remarkable generative performance by iteratively refining noisy samples through a sequence of denoising operations. An important component driving this refinement is the attention mechanism within the learned parameterization, which governs how information flows across spatial locations, semantic tokens and intermediate features. Existing training-free guidance methods often rely on score-space corrections or heuristic changes to internal activations, such as blurring attention maps. We instead guide diffusion by evolving attention through a Partial Differential Equation (PDE) inspired by Landau–de Gennes (LdG) dynamics. This energy-dissipating flow suppresses unstable attention patterns while preserving directional structure, providing a principled way to modulate the model’s internal information flow without retraining. The resulting guidance integrates cleanly with modern text-to-image samplers, requires no architectural modification, and improves generation quality both qualitatively and quantitatively. On MS-COCO, our method improves over SDXL and prior attention-based guidance methods. Under 4-bit model quantization, it improves generation quality and outperforms the unguided FP16 SDXL baseline across all reported metrics.