Diffusion models robustly adapt to low-dimensional structure across a wide range of coefficient choices, meaning practitioners don't need to fine-tune these hyperparameters precisely to get dimension-independent speedups on structured data.
This paper proves that diffusion models can efficiently sample from low-dimensional data structures regardless of how you set their update coefficients, as long as they fall within a broad class. The key finding is that sampling takes only O(k/ε) iterations (where k is the intrinsic dimension), independent of the ambient dimension—showing this efficiency isn't fragile to implementation details.