Title: Overshoot and Shrinkage in Classifier-Free Guidance: From Theory to Practice
Primary area: generative models
Keywords: Diffusion, flow-matching, classifier-free guidance

Abstract: Classifier-Free Guidance (CFG) is widely used in diffusion and flow-based generative models for high-quality conditional generation, yet its theoretical properties remain incompletely understood. By connecting CFG to the high-dimensional framework of diffusion regimes, we show that in sufficiently high dimensions it reproduces the correct target distribution—a “blessing-of-dimensionality” result. Leveraging this theoretical framework, we analyze how the well-known artifacts of mean overshoot and variance shrinkage emerge in lower dimensions, characterizing how they become more pronounced as dimensionality decreases. Building on these insights, we propose a simple nonlinear extension of CFG, proving that it mitigates both effects while preserving CFG’s practical benefits. Finally, we validate our approach through numerical simulations on Gaussian mixtures and real-world experiments on diffusion and flow-matching state-of-the-art class-conditional and text-to-image models, demonstrating continuous improvements in sample quality, diversity, and consistency.