A solvable model of learning generative diffusion: theory and insights
This provides theoretical insights into generative model failures, which is incremental for researchers in machine learning theory.
The authors tackled the problem of learning generative diffusion models on high-dimensional data with low-dimensional structure, deriving asymptotic characterizations of generated samples and their dependence on training data size, and showing how mode collapse can lead to model collapse when re-training on synthetic data.
In this manuscript, we consider the problem of learning a flow or diffusion-based generative 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.