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

TL;DR

The paper identifies that classifier-free guidance (CFG) can push sampling trajectories off the data manifold, causing unbounded error growth in iterative denoising-inversion refinements. It introduces Guided Path Sampling (GPS), which replaces unstable extrapolation with manifold-constrained interpolation on the data manifold $\mathcal{M}$, and proves that the resulting error remains strictly bounded. A dynamic, coarse-to-fine cosine schedule for guidance strength further aligns semantic injection with the model’s generation process. Empirically, GPS achieves state-of-the-art perceptual and semantic metrics across SDXL and Hunyuan-DiT backbones on benchmarks like Pick-a-Pic and GenEval, demonstrating improvedImageReward, HPS v2, and overall semantic alignment; the work emphasizes path stability as essential for effective iterative refinement.

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.

Figures (2)

• Figure 1: Visual comparison of GPS with baselines on challenging prompts. GPS demonstrates superior performance across tasks involving spatial positioning, text rendering, object counting, and attribute binding. Unlike Standard and Z-Sampling methods which suffer from artifacts or semantic misalignment, GPS maintains high fidelity and prompt adherence.
• Figure 2: Schematic illustration of GPS. Unlike standard methods that extrapolate off the manifold (red dotted line), GPS employs a manifold-constrained interpolation (green solid line) during the zigzag cycle, ensuring the sampling trajectory remains stable and errors remain bounded.

Theorems & Definitions (5)

• definition 1: Semantic Information Gain
• definition 2: Approximation Error and its Decomposition
• definition 3: Guidance Mechanisms
• theorem 1: Error Divergence of Z-Sampling
• theorem 2: Error Boundedness of GPS