On the Necessity of Guidance Decay: From Three-Phase Analysis in Gaussian Mixture Models to Dynamic Optimization

Classifier-Free Guidance (CFG) is essential for conditional diffusion, yet constant guidance scales often fail to balance alignment with over-exposure and extreme sample issues. Existing heuristic schedules, like guidance truncation, lack rigorous principles and sacrifice classification confidence, while theoretical studies remain limited to constant guidance at final denoising stages, leaving the full sampling trajectory largely unanalyzed. In this work, we provide a theoretical foundation for dynamic guidance by analyzing Gaussian Mixture Models (GMM) within a general SDE framework. We characterize the dynamics of classification confidence through three distinct stages: convergence, mixed, and divergence, and rigorously prove the impact of varying guidance scale $\omega$ at reverse time $k$. We analyze the Convergence Boundary $\Omega(k)$ as the maximum guidance scale that ensures the reverse trajectory remains within the high-density regions of the data distribution. We prove that during denoising, the permissible guidance scale $\omega$ must decay to prevent the trajectory from escaping into the divergent phase, especially at the end of the denoising. Although different noise schedules have different decay rates, we found that VP(Variance Preserving) has more stringent decay rate requirement compared to VE(Variance Exploding), which is why VP is most prone to overexposure. Specifically, $\Omega(k)$ simplifies to an exponential decay $O(e^{T-k})$ in VPSDE and an algebraic decay $O(T-k)$ in VESDE. This provides a unified explanation for why constant guidance inevitably triggers artifacts and demonstrates that guidance truncation is essentially a coarse approximations of this stability limit. We can achieve dynamic optimization based on the decay rate, which better restricts the scale within the convergence region, thereby effectively eliminating overexposure while maintaining excellent semantic alignment and improving generation quality.