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

TL;DR

This paper introduces ERK-Guid, a stiffness-aware guidance method for diffusion sampling that leverages embedded Runge-Kutta techniques to improve sample quality, especially in stiff regions.

Contribution

It proposes a novel stiffness-aware guidance mechanism using embedded Runge-Kutta methods to reduce solver errors and enhance diffusion model sampling.

Findings

ERK-Guid outperforms existing methods on synthetic and ImageNet datasets.

Stiffness detection improves the stability and quality of diffusion sampling.

Leveraging eigenvector alignment of solver errors enhances guidance effectiveness.

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 leaves solver-induced errors unaddressed. In stiff regions, the ODE trajectory changes sharply, where local truncation error (LTE) becomes a critical factor that deteriorates sample quality. Our key observation is that these errors align with the dominant eigenvector, motivating us to leverage the solver-induced error as a guidance signal. We propose Embedded Runge-Kutta Guidance (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 the popular benchmark dataset, ImageNet, demonstrate that ERK-Guid consistently outperforms state-of-the-art methods. Code is available at https://github.com/mlvlab/ERK-Guid.