How Many Directions Must a Truncated Diffusion Sampler Retain? Matching Bounds Under Power-Law Spectra
Diffusion samplers can reduce computation by generating selected spectral coordinates and filling the remaining directions with noise. How many directions must they retain? We study this question for data with power-law covariance spectra. For Gaussian data compared to a smoothed target, we prove matching bounds on the required number of retained directions, provided that the ambient dimension is sufficiently large. The truncation error depends on the combined Wiener gains of the omitted directions, regardless of the accuracy of the sampler on the retained coordinates. Keeping only directions whose signal exceeds the output noise level can therefore leave a non-vanishing error: many indiv...
| Authors | Radmehr Karimian, Ali Mohades, Johannes Lederer |
|---|---|
| Primary category | math.ST |
| Published | 7 October 2026 |
| Last updated at source | 7 October 2026 |
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