Low-dimensional adaptation of diffusion models: Convergence in total variation

Jul 14, 2026

A new preprint provides theoretical analysis showing that diffusion models such as DDIM and DDPM can efficiently adapt to data with unknown low-dimensional structure. The authors prove that, under exact score functions, the number of sampling iterations needed to achieve a given total variation distance scales with the intrinsic dimension of the data, rather than the ambient dimension. The results are extended to cases where the score function is learned from data, with kernel-based estimators shown to maintain this adaptivity under certain conditions.

Why it matters: This work offers the first rigorous theoretical evidence that diffusion models can efficiently sample from high-dimensional data with low intrinsic dimension, supporting and explaining their empirical success.

Full story at: arXiv Statistical ML ↗