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.

研究融合预训练生成模型以增强目标生成模型训练的问题，提出使用 KL 散度加权重心作为最优融合机制，其中重心权重经过最优训练以最小化适合目标群体的适当损失。研究表明，通过使用基于扩散得分方法训练辅助生成模型时，可以高效地计算最优 KL 重心权重。此外，展示了当辅助模型适合其自身任务并且辅助任务组合能很好捕捉目标时，我们的融合方法在总变异距离的样本复杂度上是无维度限制的。我们提供了融合算法的简洁计算实现，并通过涉及混合模型和图像数据集的数值实验在低数据情况下验证其效率。