Our cost measures the work done by the simulation procedure to transport samples from one point in the diffusion path to the next. Our method does not require hyperparameter tuning and adapts to the dynamics and geometry of the diffusion path. Our algorithm only involves the evaluation of the estimated Stein score, making it scalable to existing pre-trained models at inference time and online during training.

However, in certain specialized domains, such as healthcare or harmless content generation, it is nearly impossible to obtain a large volume of high-quality data that matches the downstream distribution.