Higher-variance classes are learned first in diffusion models; strong class imbalance reverses the order and imposes distinct delayed learning times on minority classes.
An Analytical Theory of Spectral Bias in the Learning Dynamics of Diffusion Models
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We develop an analytical framework for understanding how the generated distribution evolves during diffusion model training. Leveraging a Gaussian-equivalence principle, we solve the full-batch gradient-flow dynamics of linear and convolutional denoisers and integrate the resulting probability-flow ODE, yielding analytic expressions for the generated distribution. The theory exposes a universal inverse-variance spectral law: the time for an eigen- or Fourier mode to match its target variance scales as $\tau\propto\lambda^{-1}$, so high-variance (coarse) structure is mastered orders of magnitude sooner than low-variance (fine) detail. Extending the analysis to deep linear networks and circulant full-width convolutions shows that weight sharing merely multiplies learning rates -- accelerating but not eliminating the bias -- whereas local convolution introduces a qualitatively different bias. Experiments on Gaussian and natural-image datasets confirm the spectral law persists in deep MLP-based UNet. Convolutional U-Nets, however, display rapid near-simultaneous emergence of many modes, implicating local convolution in reshaping learning dynamics. These results underscore how data covariance governs the order and speed with which diffusion models learn, and they call for deeper investigation of the unique inductive biases introduced by local convolution.
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The Interplay of Data Structure and Imbalance in the Learning Dynamics of Diffusion Models
Higher-variance classes are learned first in diffusion models; strong class imbalance reverses the order and imposes distinct delayed learning times on minority classes.
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SiLD is a score-matching framework that learns both manifold projection and intrinsic density from a single objective, with proven sample complexity depending only on intrinsic dimension.
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