A solvable model of learning generative diffusion: theory and insights

Hugo Cui, Cengiz Pehlevan, Yue M. Lu

Keywords: high-dimensional asymptotics, statistical physics, diffusion model

TL;DR: We characterize the distribution of the generated samples for a solvable model of diffusion model in high dimensions, parametrized by a two-layer autoencoder.

Abstract: In this manuscript, we analyze a solvable model of flow or diffusion-based generative model. We consider the problem of learning a model parametrized by a two-layer auto-encoder, trained with online stochastic gradient descent, on a high-dimensional target density with an underlying low-dimensional manifold structure. We derive a tight asymptotic characterization of low-dimensional projections of the distribution of samples generated by the learned model, ascertaining in particular its dependence on the number of training samples. Building on this analysis, we discuss how mode collapse can arise, and lead to model collapse when the generative model is re-trained on generated synthetic data.

Primary Area: Theory (e.g., control theory, learning theory, algorithmic game theory)

Submission Number: 12909