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

arXiv: https://arxiv.org/abs/2609.31742 · HTML: https://mlsanity.com/paper/2609.31742/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 8 of its 8 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 8 of 8)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [The Unreasonable Effectiveness of Deep Evidential Regression](https://mlsanity.com/paper/2205.10060/) (2022)
- [ELVAE: Evidential Learning-Based Variational Autoencoder for Uncertainty-Aware Generation](https://mlsanity.com/paper/2608.10398/) (2026)
- [PEEL: Physics-Enabled Evidential Learning for Identifiable Uncertainty in CT Imaging](https://mlsanity.com/paper/2609.29599/) (2026)

## Abstract (arXiv)

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.