ScoreFusion: fusing score-based generative models via Kullback-Leibler barycenters

We study the problem of fusing pre-trained (auxiliary) generative models to enhance the training of a target generative model. We propose using KL-divergence weighted barycenters as an optimal fusion mechanism, in which the barycenter weights are optimally trained to minimize a suitable loss for the target population. While computing the optimal KL-barycenter weights can be challenging, we demonstrate that this process can be efficiently executed using diffusion score training when the auxiliary generative models are also trained based on diffusion score methods. Moreover, we show that our fusion method has a dimension-free sample complexity in total variation distance provided that the auxiliary models are well fitted for their own task and the auxiliary tasks combined capture the target well. The main takeaway of our method is that if the auxiliary models are well-trained and can borrow features from each other that are present in the target, our fusion method significantly improves the training of generative models. We provide a concise computational implementation of the fusion algorithm, and validate its efficiency in the low-data regime with numerical experiments involving mixtures models and image datasets.