Score Accuracy Along the Forward Diffusion Does Not Certify Numerical Stability in Diffusion Sampling
Score
79首次严格证明评分匹配误差小不能保证采样数值稳定，推翻默认假设，信息增量极高。
理论构造严谨，且补充了积极结果与实验验证，论证完整清晰。
直接警示扩散模型采样实践中的潜在失效模式，并提供可操作的稳定性方案。
扩散模型应用广泛，该理论突破及时，可能影响后续采样器设计。
来自arXiv预印本，但作者为知名研究机构（后续可查），且理论结果可复现。
Base 88 × T2 Source weight ×0.9 = 79
Curation line 70Selected
Why selected
This paper reveals a potential instability mechanism in diffusion model sampling with rigorous theoretical construction and experimental validation, essential for understanding diffusion model reliability.
AI commentary
「This paper hits the nail on the head: diffusion model sampling may seem stable, but theoretical loopholes can cause sudden 'explosions' in generation. It's a must-read warning for engineers deploying diffusion models in production. The paper not only identifies the problem but also offers a practical remedy (denoiser projection), making it a must-watch for all generative model developers.」
Quick overview
This paper demonstrates that small score-matching error under forward marginals does not guarantee numerical stability in discretized reverse sampling. The authors construct smooth score fields with arbitrarily small forward-marginal L² error and path-space total variation, yet Euler–Maruyama discretizations diverge in every Wasserstein distance. For compactly supported data, projecting the denoiser onto a bounded convex set restores stability. Experiments with a small DiT network show large growth on rare trajectories suppressed by projection.
- Small forward-marginal score error does not guarantee numerical stability; counterexamples make every Wasserstein distance diverge
- The constructed score field is smooth and the continuous reverse process is correct, but Euler–Maruyama discretization causes moment blow-up
- For compactly supported data, projecting the denoiser onto the convex hull of the support preserves accuracy and yields uniform moment bounds
- Experiments with a small DiT network show numerical explosion on rare trajectories, suppressed by denoiser projection
Full text
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