Latent Schr\"odinger Bridge Diffusion Model for Generative Learning

This paper aims to conduct a comprehensive theoretical analysis of current diffusion models. We introduce a novel generative learning methodology utilizing the Schr\"odinger 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\"odinger bridge framework. Our theoretical analysis encompasses the establishment of end-to-end error analysis for learning distributions via the latent Schr\"odinger 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.