Latent Schrödinger Bridge Diffusion Model for Generative Learning

Abstract

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.

Tasks

Reproductions