A solvable model of learning generative diffusion: theory and insights
asymptotic characterizationdiffusion-based generative modeldistribution of samplesflow-based generative modelgenerative modelhigh-dimensional target densitylow-dimensional manifold structurelow-dimensional projectionsmode collapsemodel collapseonline stochastic gradient descentsample generationsynthetic datatraining samplestwo-layer auto-encoder
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.