PEEL-DDPM: Physics-Enabled Evidential Learning for the Denoising Diffusion Probabilistic Model

2026-09-23

AI Summary

This study addresses the challenges of unidentifiability and limited physical interpretability in uncertainty quantification for diffusion models. We propose a sequential training framework that integrates a frozen measurement-conditioned denoising diffusion probabilistic model (DDPM) with normal-inverse-gamma evidential learning. This approach eliminates the need for cross-loss weighting, employs nested Monte Carlo estimation to disentangle scanner and sampler noise variances, and resolves parameter ambiguity via measurement variance, thereby enabling a physically grounded decomposition of predictive uncertainty. Experimental results demonstrate that interval coverage rates align with nominal levels, the mean squared residual closely approximates the predictive variance, and the scanner variance exhibits significant dose dependence. These findings validate both the effectiveness and the physical interpretability of the proposed method.

Abstract

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.

Problem

• Denoising Diffusion Probabilistic Model
• Normal-Inverse-Gamma regression
• Uncertainty quantification
• Identifiability
• Image reconstruction

Innovation

• Evidential Learning
• Denoising Diffusion Probabilistic Model
• Uncertainty Quantification
• Normal-Inverse-Gamma Identifiability
• Nested Monte Carlo