This paper aims to conduct a comprehensive theoretical analysis of current
diffusion models. We introduce a novel generative learning methodology
utilizing the Schr{\"o}dinger bridge diffusion model in latent space as the
framework for theoretical exploration in this domain. Our approach commences
with the pre-training of an encoder-decoder architecture using data originating
from a distribution that may diverge from the target distribution, thus
facilitating the accommodation of a large sample size through the utilization
of pre-existing large-scale models. Subsequently, we develop a diffusion model
within the latent space utilizing the Schr{\"o}dinger bridge framework. Our
theoretical analysis encompasses the establishment of end-to-end error analysis
for learning distributions via the latent Schr{\"o}dinger bridge diffusion
model. Specifically, we control the second-order Wasserstein distance between
the generated distribution and the target distribution. Furthermore, our
obtained convergence rates effectively mitigate the curse of dimensionality,
offering robust theoretical support for prevailing diffusion models.

通过在潜空间中利用 Schr {"o} dinger bridge 扩散模型构建新的生成学习方法，本文对当前扩散模型进行了全面的理论分析，包括利用预训练的编码器 - 解码器架构和 Schr {"o} dinger bridge 框架开发了潜空间中的扩散模型，通过控制生成分布和目标分布之间的二阶 Wasserstein 距离，获得了收敛速率，从而为现有的扩散模型提供了稳健的理论支持。