Error as Signal: Stiffness-Aware Diffusion Sampling via Embedded Runge-Kutta Guidance

Abstract

Classifier-Free Guidance (CFG) has established the foundation for guidance mechanisms in diffusion models, showing that well-designed guidance proxies significantly improve conditional generation and sample quality. Autoguidance (AG) has extended this idea, but it relies on an auxiliary network and leave solver-induced errors unaddresed. In stiff regions, the ODE trajectory changes sharply, where local truncation error (LTE) becomes a critical factor to deteriorate sample quality. Our key observation is that these errors align with the dominant eigenvector, motivating us to target the solver-induced error as a guidance signal. We propose **E**mbedded **R**unge–**K**utta based **Guid**ance (ERK-Guid), which exploits detected stiffness to reduce LTE and stabilize sampling. We theoretically and empirically analyze stiffness and eigenvector estimators with solver errors to motivate the design of ERK-Guid. Our experiments on both synthetic datasets and popular benchmark dataset, ImageNet, demonstrate that ERK-Guid consistently outperforms state-of-the-art methods.