Universal Local Error and Realized Amplification for the First-Order EDM Predictor

Key points

• We prove that local error admits a universal bound: for any data distribution with finite second moment, the one-step discretization error is quadratic in the step size, with an explicit constant that does not depend on the data distribution.1
• At high noise levels, we exploit the network parametrization of EDM to derive an explicit contraction criterion.1
• This analysis yields an $O(e^{ΛK}/K)$ global discretization error for $K$ sampling steps, where $ΛK$ is the low-noise log-amplification.1
• Experiments on a one-dimensional Gaussian mixture show how measured amplification accounts for slower error decay on finite sampling grids.1

Sources (1)

• [1]Universal Local Error and Realized Amplification for the First-Order EDM Predictor
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 02:54 PM

  We analyze the first-order deterministic diffusion sampler of Karras et al. (2022), termed EDM, in 2-Wasserstein distance by separating two sources of error: local discretization error and its amplification by subsequent learned steps.

  We prove that local error admits a universal bound: for any data distribution with finite second moment, the one-step discretization error is quadratic in the step size, with an explicit constant that does not depend on the data distribution.

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