Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curves

• URL: http://arxiv.org/abs/2502.00336v2
• Date: Tue, 07 Oct 2025 19:37:10 GMT
• Title: Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curves
• Authors: Anand Jerry George, Rodrigo Veiga, Nicolas Macris,
• Abstract summary: Empirical studies suggest that generalization and memorization are influenced by model complexity and the size of the training dataset.<n>We capture these behaviors by derivingally precise expressions for test and train errors of Denoising Score Matching (DSM) under a simple theoretical setting.<n>Our theoretical findings are consistent with the empirical observations.
• Score: 8.038035670274706
• License: http://creativecommons.org/licenses/by/4.0/
• 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 under a simple theoretical setting. The score function is parameterized by random features neural networks, with the target distribution being $d$-dimensional Gaussian. We operate in a regime where the dimension $d$, number of data samples $n$, and number of features $p$ tend to infinity while keeping the ratios $\psi_n=\frac{n}{d}$ and $\psi_p=\frac{p}{d}$ fixed. By characterizing the test and train errors, we identify regimes of generalization and memorization as a function of $\psi_n,\psi_p$, and $m$. Our theoretical findings are consistent with the empirical observations.

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