The paper establishes an O(ε^{-4}) sample complexity bound for score estimation in diffusion models without requiring access to the empirical risk minimizer.
Proof.Leth 0 =x, and forℓ= 0,...,L−1define the layer recursion hℓ+1=σ(Wℓhℓ+bℓ), whereW ℓ∈Rnℓ+1×nℓ,b ℓ∈Rnℓ+1, andnℓ≤Wfor hidden layers
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Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Access
The paper establishes an O(ε^{-4}) sample complexity bound for score estimation in diffusion models without requiring access to the empirical risk minimizer.