How Many Directions Must a Truncated Diffusion Sampler Retain? Matching Bounds Under Power-Law Spectra
Read the original on arXiv Machine Learning →The paper investigates how many spectral directions a truncated diffusion sampler must retain when data exhibit power‑law covariance spectra. For Gaussian data compared to a smoothed target, it establishes matching upper and lower bounds on the necessary number of retained directions, assuming a sufficiently large ambient dimension. The analysis shows that truncation error depends on the combined Wiener gains of omitted directions, meaning that even weak individual directions can collectively contribute significant error, and it provides practical guidelines for selecting the retained subspace and diffusion noise level.
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