@inproceedings{
guo2024gradient,
title={Gradient Guidance for Diffusion Models: An Optimization Perspective},
author={Yingqing Guo and Hui Yuan and Yukang Yang and Minshuo Chen and Mengdi Wang},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=X1QeUYBXke}
}
Diffusion models have demonstrated empirical successes in various applications and can be adapted to task-specific needs via guidance. This paper studies a form of gradient guidance for adapting a pre-trained diffusion model towards optimizing user-specified objectives. We establish a mathematical framework for guided diffusion to systematically study its optimization theory and algorithmic design. Our theoretical analysis spots a strong link between guided diffusion models and optimization: gradient-guided diffusion models are essentially sampling solutions to a regularized optimization problem, where the regularization is imposed by the pre-training data. As for guidance design, directly bringing in the gradient of an external objective function as guidance would  jeopardize the structure in generated samples. We investigate a modified form of gradient guidance based on a forward prediction loss, which leverages the information in pre-trained score functions and provably preserves the latent structure. We further consider an iteratively fine-tuned version of gradient-guided diffusion where guidance and score network are both updated with newly generated samples. This process mimics a first-order optimization iteration in expectation, for which we proved $\tilde{\mathcal{O}}(1/K)$ convergence rate to the global optimum when the objective function is concave. Our code is released at https://github.com/yukang123/GGDMOptim.git.
Gradient Guidance for Diffusion Models: An Optimization Perspective
Yingqing Guo Hui Yuan Yukang Yang Minshuo Chen Mengdi Wang