A solvable model of learning generative diffusion: theory and insights
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912696761319424 |
|---|---|
| author | Cui, Hugo Pehlevan, Cengiz Lu, Yue M. |
| author_facet | Cui, Hugo Pehlevan, Cengiz Lu, Yue M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03937 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A solvable model of learning generative diffusion: theory and insights Cui, Hugo Pehlevan, Cengiz Lu, Yue M. Machine Learning Disordered Systems and Neural Networks 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. |
| title | A solvable model of learning generative diffusion: theory and insights |
| topic | Machine Learning Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2501.03937 |