Towards a unified framework for guided diffusion models
This provides the first theoretical characterization of what specific performance metric classifier-free guidance improves for general target distributions, addressing a key gap in diffusion model theory.
The authors developed a unified theoretical framework for guided diffusion models that rigorously quantifies reward improvement when injecting guidance terms into the diffusion process, showing classifier-free guidance decreases the expected reciprocal of classifier probability and yielding a new easy-to-train sampler for reward-guided diffusion.
Guided or controlled data generation with diffusion models\blfootnote{Partial preliminary results of this work appeared in International Conference on Machine Learning 2025 \citep{li2025provable}.} has become a cornerstone of modern generative modeling. Despite substantial advances in diffusion model theory, the theoretical understanding of guided diffusion samplers remains severely limited. We make progress by developing a unified algorithmic and theoretical framework that accommodates both diffusion guidance and reward-guided diffusion. Aimed at fine-tuning diffusion models to improve certain rewards, we propose injecting a reward guidance term -- constructed from the difference between the original and reward-reweighted scores -- into the backward diffusion process, and rigorously quantify the resulting reward improvement over the unguided counterpart. As a key application, our framework shows that classifier-free guidance (CFG) decreases the expected reciprocal of the classifier probability, providing the first theoretical characterization of the specific performance metric that CFG improves for general target distributions. When applied to reward-guided diffusion, our framework yields a new sampler that is easy-to-train and requires no full diffusion trajectories during training. Numerical experiments further corroborate our theoretical findings.