Diffusion Removes Langevin's Conditioning Dependence: A Sharp Gaussian Analysis

arXiv:2610.12052 · stat.ML, cs.LG · Submitted 2026-10-08 · Read on arXiv

stat.ML, cs.LG

Submitted: 2026-10-08

Updated: 2026-10-08

Code: https://github.com/aperbost/diffusion-vs-Langevin

Terminology

• Diffusion Model — 21× in this paper · explained in 8 episodes
• Diffusion Models — 20× in this paper · explained in 6 episodes
• Langevin Dynamics — 12× in this paper · explained in 2 episodes
• Regularization — 8× in this paper · explained in 3 episodes
• In International Conference on Machine Learning — 5× in this paper
• Wasserstein Distance — 5× in this paper · explained in 4 episodes
• Admissibility — 3× in this paper · explained in 2 episodes
• Anisotropy — 3× in this paper · explained in 3 episodes
• Generative Modeling — 3× in this paper · explained in 3 episodes
• Adam — 2× in this paper · explained in 2 episodes
• Diffusion Processes — 2× in this paper · explained in 2 episodes
• Error Decomposition — 2× in this paper · explained in 3 episodes
• In Conference on Learning Theory — 2× in this paper
• In International Conference on Learning Representations — 2× in this paper
• Non-asymptotic Analysis — 2× in this paper · explained in 2 episodes
• 2-Wasserstein Distance — 1× in this paper · explained in 1 episode
• Accuracy — 1× in this paper · explained in 1 episode
• Admissibility Conditions — 1× in this paper · explained in 1 episode
• Generalization — 1× in this paper · explained in 13 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Models — 1× in this paper · explained in 2 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Scaling Laws — 1× in this paper · explained in 4 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes
• Uncertainty Quantification — 1× in this paper · explained in 8 episodes

Sources

• Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance
• From Score Matching to Diffusion: A Fine-Grained Error Analysis in the Gaussian Setting
• Geometry-Aware Discretization Error of Diffusion Models

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