This paper demonstrates that diffusion models' ability to exploit low-dimensional structure for accelerated sampling is a robust property independent of specific update coefficient choices. The authors prove that a broad class of coefficients allows generating an ε-accurate sample in O(k/ε) iterations, regardless of ambient dimension.
- Adaptation to low-dimensional structure is shown to be robust across a wide range of update coefficients.
- Theoretical proof establishes that O(k/ε) iterations suffice for ε-accuracy in total variation distance.
- The result holds independently of the ambient dimension of the data.
- The framework broadens the class of diffusion samplers known to benefit from low-dimensional adaptation.
These findings provide a theoretical justification for the empirical effectiveness of various diffusion samplers when applied to structured, high-dimensional data.