From Score Approximation to Distribution Approximation in Score-Based Diffusion Models
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TL;DR - This paper proves that accurate neural-network approximation of a diffusion model’s score function yields a quantitatively close generated distribution in KL divergence. It connects classical score approximation guarantees to end-to-end generative accuracy.
- The KL-error bound depends explicitly on score approximation error, the diffusion noise schedule, and terminal prior mismatch.
- A residual error remains when the forward process’s terminal distribution differs from the reverse process’s initialization prior.
- The proof combines Hornik’s universal approximation theorem, Girsanov’s theorem on path space, and the data processing inequality.
- The analysis is approximation-theoretic rather than based on finite-sample statistics or structural assumptions about the data.
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From Score Approximation to Distribution Approximation in Score-Based Diffusion Models
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TL;DR - This paper proves that accurate neural-network approximation of a diffusion model’s score function yields a quantitatively close generated distribution in KL divergence. It connects classical score approximation guarantees to end-to-end generative accuracy.
- The KL-error bound depends explicitly on score approximation error, the diffusion noise schedule, and terminal prior mismatch.
- A residual error remains when the forward process’s terminal distribution differs from the reverse process’s initialization prior.
- The proof combines Hornik’s universal approximation theorem, Girsanov’s theorem on path space, and the data processing inequality.
- The analysis is approximation-theoretic rather than based on finite-sample statistics or structural assumptions about the data.