C$^2$FG: Control Classifier-Free Guidance via Score Discrepancy Analysis

TL;DR

This paper provides a theoretical foundation for classifier-free guidance in diffusion models, introduces a new control method called C$^2$FG that adapts guidance dynamically, and demonstrates its effectiveness across tasks.

Contribution

It offers a rigorous analysis of guidance dynamics, proposes a novel time-dependent guidance method, and shows its broad applicability without additional training.

Findings

C$^2$FG improves guidance effectiveness across tasks.

Theoretical bounds explain limitations of fixed guidance weights.

C$^2$FG is compatible with existing strategies.

Abstract

Classifier-Free Guidance (CFG) is a cornerstone of modern conditional diffusion models, yet its reliance on the fixed or heuristic dynamic guidance weight is predominantly empirical and overlooks the inherent dynamics of the diffusion process. In this paper, we provide a rigorous theoretical analysis of the Classifier-Free Guidance. Specifically, we establish strict upper bounds on the score discrepancy between conditional and unconditional distributions at different timesteps based on the diffusion process. This finding explains the limitations of fixed-weight strategies and establishes a principled foundation for time-dependent guidance. Motivated by this insight, we introduce \textbf{Control Classifier-Free Guidance (C$^2$FG)}, a novel, training-free, and plug-in method that aligns the guidance strength with the diffusion dynamics via an exponential decay control function. Extensive experiments demonstrate that C$^2$FG is effective and broadly applicable across diverse generative tasks, while also exhibiting orthogonality to existing strategies.