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.
ProofPaper ↗
Key points
- 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.
- Combining this characterization with a diffusion convergence bound yields sufficient sampling-step complexity under exact scores.
Sources (1)
- [1]How Many Directions Must a Truncated Diffusion Sampler Retain? Matching Bounds Under Power-Law SpectraarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 02:32 PM
Diffusion samplers can reduce computation by generating selected spectral coordinates and filling the remaining directions with noise.
How many directions must they retain?
Extractive summary: sentences quoted from the sources.