Score Accuracy Along the Forward Diffusion Does Not Certify Numerical Stability in Diffusion Sampling

arXiv:2607.08757 · stat.ML, cs.LG, math.NA, math.PR · Submitted 2026-07-09 · Read on arXiv

Yiwei Zhou

stat.ML, cs.LG, math.NA, math.PR

Submitted: 2026-07-09

Comments: 27 pages, 2 figures, 1 table

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Accuracy — 18× in this paper · explained in 1 episode
• Diffusion Model — 11× in this paper · explained in 10 episodes
• Diffusion Models — 10× in this paper · explained in 9 episodes
• Transformer — 4× in this paper · explained in 2 episodes
• Wasserstein Distance — 3× in this paper · explained in 6 episodes
• Convergence Guarantees — 2× in this paper · explained in 3 episodes
• Embeddings — 2× in this paper · explained in 2 episodes
• Generative Model — 2× in this paper · explained in 2 episodes
• Generative Modeling — 2× in this paper · explained in 3 episodes
• Generative Models — 2× in this paper · explained in 3 episodes
• Localization — 2× in this paper · explained in 2 episodes
• Calibration — 1× in this paper · explained in 9 episodes
• Composition — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Decode — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Generator — 1× in this paper · explained in 2 episodes
• Langevin Dynamics — 1× in this paper · explained in 3 episodes
• Parameterization — 1× in this paper · explained in 2 episodes
• Residual Connections — 1× in this paper · explained in 3 episodes
• Robustness — 1× in this paper · explained in 6 episodes
• Score Function — 1× in this paper · explained in 4 episodes
• Transformers — 1× in this paper · explained in 2 episodes

Sources

• On the Robustness of Langevin Dynamics to Score Function Error
• Diffusion Models Observe Only Gradients: A Geometric Perspective on Score Matching Errors
• Contractive Diffusion Probabilistic Models
• Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding

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