Establishes the first minimax-optimal generalization bounds for gradient-descent-trained neural networks performing denoising score matching in diffusion models.
(42) Hence, we have E [∥H(τ) − H(0)∥F ] ≤ ∑ i,k,j,ℓ E [⏐ ⏐Hik jℓ (τ) − Hik jℓ (0) ⏐ ⏐] ≤ 4(dN )2RwC3 max √ 2π ∆ + 2(dN )2C2 max m δ
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Neural Network-Based Score Estimation in Diffusion Models: Optimization and Generalization
Establishes the first minimax-optimal generalization bounds for gradient-descent-trained neural networks performing denoising score matching in diffusion models.