Yukang Yang

Yingqing Guo, Hui Yuan, Yukang Yang et al.

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 O(1/K) convergence rate to the global optimum when the objective function is concave. Our code will be released at https://github.com/yukang123/GGDMOptim.git.

Yingqing Guo, Yukang Yang, Hui Yuan et al.

Training-free guidance enables controlled generation in diffusion and flow models, but most methods rely on gradients and assume differentiable objectives. This work focuses on training-free guidance addressing challenges from non-differentiable objectives and discrete data distributions. We propose TreeG: Tree Search-Based Path Steering Guidance, applicable to both continuous and discrete settings in diffusion and flow models. TreeG offers a unified framework for training-free guidance by proposing, evaluating, and selecting candidates at each step, enhanced with tree search over active paths and parallel exploration. We comprehensively investigate the design space of TreeG over the candidate proposal module and the evaluation function, instantiating TreeG into three novel algorithms. Our experiments show that TreeG consistently outperforms top guidance baselines in symbolic music generation, small molecule design, and enhancer DNA design with improvements of 29.01%, 16.6%, and 18.43%. Additionally, we identify an inference-time scaling law showing TreeG's scalability in inference-time computation.