PEEL-DDPM：用于去噪扩散概率模型的物理启发的证据学习
PEEL-DDPM: Physics-Enabled Evidential Learning for the Denoising Diffusion Probabilistic Model
AI总结：
提出PEEL-DDPM框架，通过物理启发的证据学习解决NIG回归不可识别问题，实现扩散模型重建中可解释的不确定性分解，实验验证了其校准性和物理一致性。
AI中文摘要：
正态-逆伽马（NIG）回归无法从其边缘学生t似然中识别：四个NIG参数中确定三个组合，留下一个自由度。我们提出了PEEL-DDPM，一种用于去噪扩散概率模型的物理启发的证据学习框架。首先使用epsilon-MSE训练一个测量条件的DDPM，然后将其冻结。其完整的反向轨迹产生重建结果，该重建结果与已知训练对象的残差由最终图像证据网络建模。该网络仅学习可识别的学生t坐标，而重复的扫描仪噪声实现和重复的扩散轨迹提供了最终图像偶然方差的嵌套蒙特卡洛估计，该方差被分离为扫描仪引起的和采样器引起的成分。该测量方差解决了剩余的NIG模糊性，并产生了将预测不确定性分解为测量、扩散和认知项的结果。该方法使用顺序训练，无需交叉损失加权系数。在八项保留对象的可行性研究中，经验中心区间覆盖率在标称50%、80%、90%和95%区间下分别为49.3%、80.3%、90.1%和95.6%。均方残差为平均预测方差的0.967倍，单图像偶然性头部与独立嵌套参考的合并Spearman相关性为0.785。在五个剂量水平下，扫描仪引起的方差显示对数-对数剂量斜率为-1.15，而采样器引起的方差几乎与剂量无关，斜率为-0.01。这些结果支持PEEL-DDPM作为基于扩散的图像重建中可识别且物理可解释的不确定性量化的实用途径。
英文摘要：
Normal-inverse-gamma (NIG) regression is not identifiable from its marginal Student-t likelihood: three combinations of four NIG parameters are determined, leaving one degree of freedom. We introduce PEEL-DDPM, a physics-enabled evidential learning framework for denoising diffusion probabilistic models. A measurement-conditioned DDPM is first trained with epsilon-MSE and then frozen. Its complete reverse trajectory produces a reconstruction, whose residual from the known training object is modeled by a final-image evidential network. The network learns only the identifiable Student-t coordinates, while repeated scanner-noise realizations and repeated diffusion trajectories provide a nested Monte Carlo estimate of final-image aleatoric variance, separated into scanner-induced and sampler-induced components. This measured variance resolves the remaining NIG ambiguity and yields a decomposition of predictive uncertainty into measurement, diffusion, and epistemic terms. The method uses sequential training without a cross-loss weighting coefficient. In a feasibility study on eight held-out objects, empirical central-interval coverages were 49.3%, 80.3%, 90.1%, and 95.6% for nominal 50%, 80%, 90%, and 95% intervals. The mean squared residual was 0.967 times the mean predicted variance, and a single-image aleatoric head achieved pooled Spearman correlation 0.785 against an independent nested reference. Across five dose levels, scanner-induced variance showed a log-log dose slope of -1.15, whereas sampler-induced variance remained nearly dose independent with slope -0.01. These results support PEEL-DDPM as a practical route to identifiable and physically interpretable uncertainty quantification in diffusion-based image reconstruction.
