Latent Schr\"odinger Bridge Diffusion Model for Generative Learning
<|reference_start|>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{\"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.<|reference_end|>
@article{jiao2024latent,
    title={Latent Schr{\"o}dinger Bridge Diffusion Model for Generative Learning},
    author={Yuling Jiao, Lican Kang, Huazhen Lin, Jin Liu, Heng Zuo},
    journal={arXiv preprint arXiv:2404.13309},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.13309},
    primaryClass={stat.ML cs.LG}
}