Score Accuracy Along the Forward Diffusion Does Not Certify Numerical Stability in Diffusion Sampling
Score matching controls average error under the forward marginals, but a discretized reverse-time sampler evaluates the learned score along its own trajectory. We show that small forward-marginal error does not guarantee numerical stability. We construct a single smooth score field with arbitrarily small forward-marginal $L^2$ error. The learned reverse-time process is nonexplosive, has moments of every order, and can be arbitrarily close to the exact reverse-time process in path-space total variation. Yet its Euler--Maruyama discretizations converge in probability while every positive moment
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- PossiblePossibly related (embedding) · 51%Understand diffusion in 20 minutes →
- PossiblePossibly related (embedding) · 46%Diffusion →
- FuzzySimilar title/name (fuzzy) · 59%stabilityai/stable-diffusion-xl-base-1.0 →
“Fuzzy title match (0.73): “Score Accuracy Along the Forward Diffusion Does Not Certify ” ≈ “stabilityai/stable-diffusion-xl-base-1.0””
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- FuzzySimilar title/name (fuzzy) · 59%stabilityai/stable-diffusion-3.5-large →
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- LinkedLinked via arxiv author · 85%Yiwei Zhou →
“Score Accuracy Along the Forward Diffusion Does Not Certify Numerical Stability in Diffusion Sampling”
- FuzzyOverlapping authors or contributors · 62%sgl-project/sglang →
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