Latent Schr{\"o}dinger Bridge Diffusion Model for Generative Learning

TL;DR

This paper introduces a latent Schr{"o}dinger bridge diffusion model for generative learning, providing a comprehensive theoretical analysis and error bounds that improve understanding and performance of diffusion models in high-dimensional spaces.

Contribution

The paper presents a novel latent Schr{"o}dinger bridge diffusion framework with theoretical error analysis, including convergence rates that address the curse of dimensionality.

Findings

Established end-to-end error bounds for the model.

Controlled Wasserstein distance between generated and target distributions.

Provided convergence rates that mitigate high-dimensional challenges.

Abstract

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.