弱扩散先验也能高效解决逆问题，关键看观测数据是否足够丰富。
Weak Diffusion Priors Can Still Achieve Strong Inverse-Problem Performance
- 用低质量或不匹配的扩散模型作先验，仍可有效求解逆问题。
- 当观测像素多、信息量大时，弱先验性能接近全精度模型。
- 适用于数据观测充分但缺乏高质量先验的场景，如医学成像重建。
扩散模型常作为逆问题的先验，传统方法依赖与目标信号高度匹配的高保真模型。然而实践中常需使用不匹配或低质量的先验。令人惊讶的是，这些弱先验往往表现接近全强度、同域基线。本文通过大量实验研究弱先验在何种条件下有效：当测量高度信息丰富（如观测像素众多）时表现良好，反之则失败。结合贝叶斯一致性理论与局部相关性分析，揭示高维测量使后验集中于真实信号的条件，并发现弱先验与强先验在局部空间结构上具有相似性。该结果为弱扩散先验的可靠使用提供了理论依据。代码已公开于 https://github.com/jjia131/weak-diffusion-priors-inverse-problem。
原文摘要 · Abstract (English)
Can a diffusion model trained on bedrooms recover human faces? Diffusion models are widely used as priors for inverse problems, but standard approaches usually assume a high-fidelity model trained on data that closely match the unknown signal. In practice, one often must use a mismatched or low-fidelity diffusion prior. Surprisingly, these weak priors often perform nearly as well as full-strength, in-domain baselines. We study when and why inverse solvers are robust to weak diffusion priors. Through extensive experiments, we find that weak priors succeed when measurements are highly informative (e.g., many observed pixels), and we identify regimes where they fail. To explain this behavior, we combine Bayesian-consistency theory with local-correlation analysis: the theory gives conditions under which high-dimensional measurements make the posterior concentrate near the true signal, while the correlation analysis shows that weak and stronger natural-image priors can share similar local spatial structure. These results provide a principled justification on when weak diffusion priors can be used reliably. Code is available at https://github.com/jjia131/weak-diffusion-priors-inverse-problem.
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