Universal Local Error and Realized Amplification for the First-Order EDM Predictor
stat.ML, cs.LG
Submitted: 2026-10-07
Updated: 2026-10-07
Comments: 71 pages; code: https://github.com/nbrosse/edm-error-propagation-code
Code: https://github.com/nbrosse/edm-error-propagation-code
License: http://creativecommons.org/licenses/by/4.0/
The gist: We analyze the first-order deterministic diffusion sampler of Karras et al.
Terminology
Abstract
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. Error propagation, in contrast, depends on the learned network. At high noise levels, we exploit the network parametrization of EDM to derive an explicit contraction criterion. At low noise levels, we measure propagation through the amplification realized on the distributions transported by the sampler; this realized amplification can be arbitrarily smaller than the worst-case Lipschitz constant. This analysis yields an O(e Λ K/K) global discretization error for K sampling steps, where Λ K is the low-noise log-amplification. Experiments on a one-dimensional Gaussian mixture show how measured amplification accounts for slower error decay on finite sampling grids. Diagnostics on a pretrained CIFAR-10 model illustrate related stability mechanisms without certifying the global assumptions.
Sources
- Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
- Error Bounds for Flow Matching Methods
- Nearly $d$-Linear Convergence Bounds for Diffusion Models via Stochastic Localization
- Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance
- Boundary-layer asymptotics for Gaussian-smoothed singular measures
- Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradients
- Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplers
- Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions
- The probability flow ODE is provably fast
- Lipschitz-Guided Design of Interpolation Schedules in Generative Models
- Convergence of denoising diffusion models under the manifold hypothesis
- Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distances
- Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distance
- An Introduction to Flow Matching and Diffusion Models
- Disentangling Total-Variance and Signal-to-Noise-Ratio Improves Diffusion Models
- Elucidating the Design Space of Diffusion-Based Generative Models
- Wasserstein bounds for denoising diffusion probabilistic models via the F\"ollmer process
- Non-asymptotic error bounds for probability flow ODEs under weak log-concavity
- Score-based Generative Modeling Secretly Minimizes the Wasserstein Distance
- Convergence of score-based generative modeling for general data distributions
Related papers
- Behavior of prediction performance metrics with rare events
- Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs
- A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
- Scalable Posterior Uncertainty for Flexible Density-Based Clustering
- Efficient quadratic entropy with distance sketches
- Embedding-Bias in Conditional Independence Testing