Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curves
arXiv:2502.00336v3 Announce Type: replace Abstract: We theoretically investigate the phenomena of generalization and memorization in diffusion models. Empirical studies suggest that these phenomena are influenced by model complexity and the size of the training dataset. In our experiments, we further observe that the number of noise samples per data sample ($m$) used during Denoising Score Matching (DSM) plays a significant and non-trivial role. We capture these behaviors and shed insights into their mechanisms by deriving asymptotically precise expressions for test and train errors of DSM und
The proliferation of diffusion models in generative AI makes understanding their fundamental mechanisms of generalization and memorization crucial for future development.
This research provides theoretical insights into the learning dynamics of diffusion models, which could lead to more efficient, robust, and controllable AI systems.
A deeper understanding of how model complexity, data size, and noise sampling affect diffusion model performance offers pathways to optimize their training and application.
- · AI Researchers
- · Generative AI Developers
- · Machine Learning Frameworks
- · Inefficient Diffusion Model Architectures
Improved understanding of diffusion model generalization and memorization through precise learning curves.
Development of more resource-efficient and performant diffusion models with better control over output quality.
Acceleration of generative AI applications across various industries due to predictable and controllable model behavior.
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