First Learn, Then Memorize: The Spectral Bias of Diffusion Models

arXiv:2609.35377 · cs.LG, cond-mat.dis-nn · Submitted 2026-09-28 · Read on arXiv

cs.LG, cond-mat.dis-nn

Submitted: 2026-09-28

Updated: 2026-09-28

Terminology

• Diffusion Model — 1× in this paper · explained in 9 episodes
• Diffusion Models — 1× in this paper · explained in 6 episodes

Sources

• Losing dimensions: Geometric memorization in generative diffusion
• On Lazy Training in Differentiable Programming
• Biased Generalization in Diffusion Models
• The Gaussian equivalence of generative models for learning with shallow neural networks
• Generalization, memorization, and overfitting for diffusion models trained in the lazy high-dimensional regime
• On the Generalization Properties of Diffusion Models
• A Good Score Does not Lead to A Good Generative Model
• Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow
• An Equivalence Principle for the Spectrum of Random Inner-Product Kernel Matrices with Polynomial Scalings
• The generalization error of random features regression: Precise asymptotics and double descent curve
• Generalization Dynamics of Linear Diffusion Models
• Local Coverage Governs Memorization in Diffusion Models
• Spectrum of inner-product kernel matrices in the polynomial regime and multiple descent phenomenon in kernel ridge regression
• Universality of Kernel Random Matrices and Kernel Regression in the Quadratic Regime
• Asymptotics of Non-Convex Generalized Linear Models in High-Dimensions: A proof of the replica formula
• An Analytical Theory of Spectral Bias in the Learning Dynamics of Diffusion Models
• Kernel ridge regression under power-law data: spectrum and generalization

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