A precise asymptotic analysis of learning diffusion models: theory and insights

• URL: http://arxiv.org/abs/2501.03937v1
• Date: Tue, 07 Jan 2025 16:56:40 GMT
• Title: A precise asymptotic analysis of learning diffusion models: theory and insights
• Authors: Hugo Cui, Cengiz Pehlevan, Yue M. Lu,
• Abstract summary: We consider the problem of learning a flow or diffusion-based generative model parametrized by a two-layer auto-encoder. We derive a tight characterization of low-dimensional projections of the distribution of samples generated by the learned model.
• Score: 37.30894159200853
• License:
• Abstract: 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.

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