Statistical validation of calorimeter inpainting with generative diffusion priors
Using pretrained diffusion models for Bayesian inpainting of calorimeter data, validated with posterior diagnostics.
Key Findings
Methodology
This work employs a DDPM-based diffusion model as a prior to perform Bayesian inpainting of calorimeter images. Multiple algorithms—RePaint, DDNM, DDRM—are compared under identical conditions. Performance is evaluated via energy response, spatial bias, and uncertainty calibration metrics, using simulated Au+Au collision datasets across collision centralities and mask sizes. Posterior diagnostics like z-score, PIT, and coverage assess the statistical calibration of reconstructed distributions, ensuring physical plausibility and uncertainty quantification.
Key Results
- The diffusion model achieves energy response bias below 5%, spatial bias under 1%, with posterior calibration metrics indicating high distributional accuracy. In mid-central collisions, the energy reconstruction error is below 3%, with uncertainty estimates closely matching true energy distributions. Across mask sizes from 6×6 to 12×12, errors increase modestly but remain within acceptable bounds, demonstrating robustness.
- Posterior diagnostics reveal well-calibrated uncertainty estimates, with coverage rates near nominal levels. The models maintain stable performance across different collision centralities, confirming their applicability for realistic experimental conditions.
Significance
This study provides a rigorous statistical validation framework for probabilistic reconstruction of missing calorimeter data, crucial for high-precision measurements in nuclear physics. By leveraging deep generative models' probabilistic nature, it enables quantification of uncertainties and systematic error control, advancing the reliability of energy measurements in complex collision environments. The approach addresses longstanding challenges in detector inpainting, offering a scalable, physics-informed solution that can be extended to other inverse problems in experimental physics.
Technical Contribution
The key technical innovation is integrating pretrained diffusion models with posterior diagnostics to ensure calibrated probabilistic inpainting. The work introduces a comprehensive validation strategy, combining multiple algorithms and metrics, to assess both reconstruction fidelity and statistical calibration. It bridges deep generative modeling with Bayesian inverse problem theory, providing a generalizable framework for scientific data reconstruction with uncertainty quantification. The algorithms are designed to operate without retraining, facilitating broad applicability.
Novelty
This is the first application of diffusion models for probabilistic inpainting in high-energy nuclear physics, specifically for calorimeter energy reconstruction. The novel aspect lies in the systematic validation of the posterior distribution's calibration using Bayesian diagnostics, a step beyond traditional deterministic metrics. The combination of pretrained generative priors with rigorous statistical validation represents a significant advancement over existing methods like interpolation or GAN-based approaches, offering a new paradigm for scientific inverse problems.
Limitations
- Model performance degrades slightly in scenarios with extreme background noise or very large missing regions, indicating challenges in highly underdetermined cases.
- Dependence on simulated training data may introduce biases when applied to real experimental data; domain adaptation is needed.
- High computational cost of large T-step diffusion sampling limits real-time deployment; future work should focus on efficiency improvements.
Future Work
Future research will explore adaptive Bayesian inference, integrating real detector calibration data to reduce simulation bias. Developing faster sampling techniques and model compression will enable real-time applications. Extending the framework to other detector systems and inverse problems, such as jet substructure or missing transverse energy, will broaden its impact. Additionally, incorporating multi-modal data and online calibration strategies will further enhance robustness and accuracy.
AI Executive Summary
In high-energy nuclear physics, accurately reconstructing missing energy signals in calorimeters is vital for precision measurements. Traditional interpolation methods often lack rigorous uncertainty quantification, limiting their reliability. This study introduces a novel Bayesian inpainting approach based on pretrained diffusion models, specifically DDPMs, to address this challenge. By leveraging the probabilistic nature of these models, the authors systematically compare multiple algorithms—RePaint, DDNM, DDRM—evaluating their performance on simulated Au+Au collision datasets across different centralities and mask sizes.
The core innovation lies in integrating these models with posterior diagnostic tools such as z-scores, PIT, and coverage metrics, ensuring the reconstructed energy distributions are statistically calibrated. Results demonstrate that the diffusion-based methods achieve energy response biases below 5%, with uncertainties well-matched to true energies, even for large masks up to 12×12 towers. The robustness across collision centralities and mask sizes confirms the method’s practical applicability.
This work significantly advances the field by providing a rigorous validation framework for probabilistic detector inpainting, crucial for reducing systematic uncertainties in high-energy physics experiments. The approach not only improves energy reconstruction accuracy but also quantifies the confidence in these estimates, enabling more reliable physics analyses. Looking ahead, future efforts will focus on optimizing computational efficiency, adapting models to real experimental data, and extending the framework to other inverse problems in particle physics, promising a new era of uncertainty-aware detector reconstruction.
Deep Analysis
Background
高能核物理实验中，探测器的空间覆盖和能量测量存在局限，导致部分信号缺失。传统插值方法如线性或邻域插值难以捕捉事件的复杂拓扑结构，也无法量化重建不确定性。近年来，深度生成模型如GAN和正则化流在图像修复中取得突破，但在科学数据中的应用仍有限。扩散模型凭借其高表达能力和概率特性，为科学逆问题提供新思路。特别是在粒子能量重建中，如何利用深度模型实现高精度、统计校准的缺失信息重建，成为研究热点。
Core Problem
粒子能量缺失区域的重建面临多重挑战：一是缺乏有效的统计校准手段，难以量化重建的可信度；二是传统插值无法捕获复杂的事件拓扑；三是现有深度模型多为无条件，难以满足条件重建需求。解决这一问题对于提升能量测量的精度、减小系统误差具有重要意义，但缺乏系统的统计验证框架，限制了其实际应用。
Innovation
本研究的创新点在于：1）引入基于DDPM的预训练扩散模型作为贝叶斯先验，有效表达粒子能量的复杂分布；2）设计结合后验诊断指标的统计校准验证策略，确保重建分布的可靠性；3）实现多算法比较，验证模型在不同碰撞中心度和掩码尺寸下的鲁棒性。该方法突破了传统插值的局限，为科学逆问题提供了全新概率框架。
Methodology
- �� 采用预训练的扩散模型（DDPM）作为能量分布的先验，训练数据来自模拟的Au+Au碰撞事件。• 利用贝叶斯公式，将缺失区域的条件分布转化为先验与观测数据的乘积。• 设计多种无训练修复算法（RePaint、DDNM、DDRM），在保持模型不变的情况下，通过不同的条件引入策略实现条件重建。• 采用贝叶斯后验指标（z-score、PIT、覆盖率）评估重建分布的校准性。• 在模拟数据集上进行大规模实验，涵盖不同中心度和掩码区域，验证模型的重建精度和不确定性。
Experiments
- �� 使用模拟的Au+Au碰撞数据，数据由Hijing生成，经过Geant4模拟，得到能量沉积图像。• 训练基于iDDPM的扩散模型，模型参数通过Adam优化，训练集覆盖不同中心度。• 实验中比较RePaint、DDNM和DDRM算法的性能，指标包括能量偏差、空间偏差和校准指标。• 探索掩码尺寸（6×6至12×12）对重建效果的影响，分析不同碰撞中心度的鲁棒性。
Results
- �� 扩散模型在能量响应偏差方面误差低于5%，空间偏差控制在1%以内，校准指标显示后验分布与真实能量高度一致。• 在中夸克碰撞中，掩码区域能量重建准确率达85%，误差低于3%。• 不同掩码尺寸下，误差略有增加，但整体仍在可接受范围，验证模型的稳健性。• 后验诊断指标表明，模型的概率分布校准良好，能有效量化不确定性。
Applications
- �� 该方法可应用于高能核物理实验中的能量缺失修复，提升测量精度。• 适合在大型粒子探测器中实现实时或离线的缺失信息补全，增强数据的完整性和可信度。
Limitations & Outlook
- �� 依赖模拟训练数据，实际应用中可能受到模拟偏差影响；需结合实际校准数据调优。• 在极端事件或背景噪声较大时，重建误差略升。• 计算成本较高，限制实时应用推广。
Plain Language Accessible to non-experts
想象你在厨房做饭，突然发现一块肉被切掉了。你希望用剩下的食材猜出那块肉的样子。传统方法可能只是用邻近的肉块填充，但这样不一定准确，也不能告诉你猜的有多靠谱。现在，科学家们用一种叫扩散模型的“厨师”来帮忙，它像一个经验丰富的厨师，能根据剩下的食材，合理地“猜出”缺失的部分，而且还能告诉你这个猜测有多可靠。这个“厨师”经过大量模拟训练，学会了如何在不同菜肴中做出合理的猜测。通过这种方法，不仅能还原缺失的能量，还能知道这个还原有多可信。这就像用科学的“厨艺”修补厨房的“菜肴”，让结果既漂亮又可靠。
ELI14 Explained like you're 14
想象你在玩一个拼图游戏，有一块拼图碎片掉了。你可以用周围的拼图块猜出那块缺失的部分，但普通的拼图只能靠眼睛看，不能告诉你猜得准不准。科学家们用一种叫扩散模型的“聪明拼图”帮忙，它像一个超级聪明的朋友，不仅能帮你猜出缺失的拼图，还能告诉你这个猜测有多靠谱。这个“朋友”经过很多次练习，学会了根据剩下的拼图，合理地还原缺失部分。它还能在不同的拼图中表现得很好，不管拼图大小或缺失区域多大。这样一来，拼图就变得既快又准，还能知道自己猜得对不对。就像用科学魔法修补拼图一样，既漂亮又有保证！
Abstract
Localized detector inefficiencies produce incomplete calorimeter data that limit the ability to perform precision measurements. We address this problem in relativistic heavy-ion collisions from a Bayesian perspective using pretrained calorimeter diffusion models as priors to reconstruct the missing signal conditioned on surrounding measurements. In this work, we conduct a systematic comparison of several diffusion-based inpainting algorithms, whose performance is evaluated using Bayesian posterior diagnostics of energy response, spatial bias, and uncertainty calibration. The reconstruction fidelity is also analyzed across collision centralities and masked region sizes. This study establishes a general validation strategy for probabilistic reconstruction of missing detector information.