Denoising Score Matching in Diffusion Models: The Effect of Rank Constraints on Generalization
Architectural biases restrict the class of functions that a diffusion score network can represent, but their effect on generalization remains poorly understood. We study denoising score matching with score networks having a rank constrained non-linear term and a linear skip connection. Numerical experiments with trainable three-layer networks on data supported on an embedded sphere show that increasing rank lowers training error, but its effect on test error depends on sample size and data dimension. To explain this behavior, we analyze a random-feature score model under rank constraint with Gaussian data supported on a low-dimensional subspace. We characterize the optimal rank-constraine...
| Authors | Anand Jerry George, Nicolas Macris |
|---|---|
| Primary category | cs.LG |
| Published | 14 October 2026 |
| Last updated at source | 14 October 2026 |
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