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.

翻译：在卧室数据集上训练的扩散模型能否恢复人脸图像？扩散模型被广泛用作逆问题的先验，但标准方法通常假设模型在接近未知信号的数据上训练且具有高保真度。实践中，人们常需使用不匹配或低保真度的扩散先验。令人惊讶的是，这些弱先验往往能与全强度、领域内基线方法表现相当。我们研究了逆问题求解器何时及为何对弱扩散先验具有鲁棒性。通过大量实验，我们发现当测量信息高度丰富时（如观测像素数量较多），弱先验能够成功，同时我们也识别出其失效的机制。为解释这一行为，我们将贝叶斯一致性理论与局部相关性分析相结合：该理论给出了高维测量使后验分布集中于真实信号附近的条件，而相关性分析表明弱先验与更强的自然图像先验共享相似的局部空间结构。这些结果为弱扩散先验的可靠使用提供了理论依据。代码见 https://github.com/jjia131/weak-diffusion-priors-inverse-problem。