Denoising growth complexity: Data geometry and certified schedules for diffusion sampling
Two central challenges in diffusion-based sampling are the theoretical one of understanding their remarkable effectiveness even in high-dimensional settings, and the practical one of designing algorithms with certified performance guarantees. We show that these questions are intimately connected via the \emph{denoising growth complexity} ($\mathsf{DGC}$). It is a geometric measure defined by a log-time weighted integral of the derivative of the denoising mean-squared error along the Gaussian heat flow. We show how the $\mathsf{DGC}$ increments lead to a simple and explicit bound on the KL error of an Euler scheme applied to the stochastic innovations representation. The bound is local alo...
| Authors | Martin J. Wainwright |
|---|---|
| Primary category | math.ST |
| Published | 28 July 2026 |
| Last updated at source | 28 July 2026 |
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