Guided Path Sampling: Steering Diffusion Models Back on Track with Principled Path Guidance

TL;DR

This paper introduces Guided Path Sampling (GPS), a novel iterative refinement method for diffusion models that maintains the sampling path on the data manifold, improving stability, quality, and semantic adherence in generated images.

Contribution

GPS replaces unstable extrapolation with manifold-constrained interpolation, ensuring bounded errors and stable refinement, with an adaptive guidance schedule for better image quality and semantic accuracy.

Findings

GPS outperforms existing methods in perceptual quality metrics.

GPS achieves higher semantic alignment accuracy on GenEval.

GPS demonstrates improved stability and quality on SDXL and Hunyuan-DiT backbones.

Abstract

Iterative refinement methods based on a denoising-inversion cycle are powerful tools for enhancing the quality and control of diffusion models. However, their effectiveness is critically limited when combined with standard Classifier-Free Guidance (CFG). We identify a fundamental limitation: CFG's extrapolative nature systematically pushes the sampling path off the data manifold, causing the approximation error to diverge and undermining the refinement process. To address this, we propose Guided Path Sampling (GPS), a new paradigm for iterative refinement. GPS replaces unstable extrapolation with a principled, manifold-constrained interpolation, ensuring the sampling path remains on the data manifold. We theoretically prove that this correction transforms the error series from unbounded amplification to strictly bounded, guaranteeing stability. Furthermore, we devise an optimal scheduling strategy that dynamically adjusts guidance strength, aligning semantic injection with the model's natural coarse-to-fine generation process. Extensive experiments on modern backbones like SDXL and Hunyuan-DiT show that GPS outperforms existing methods in both perceptual quality and complex prompt adherence. For instance, GPS achieves a superior ImageReward of 0.79 and HPS v2 of 0.2995 on SDXL, while improving overall semantic alignment accuracy on GenEval to 57.45%. Our work establishes that path stability is a prerequisite for effective iterative refinement, and GPS provides a robust framework to achieve it.