Photomultiplier tubes (PMTs) are widely employed in particle and nuclear physics experiments. The accuracy of PMT waveform reconstruction directly impacts the detector's spatial and energy resolution. A key challenge arises when multiple photons arrive within a few nanoseconds, making it difficult to resolve individual photoelectrons (PEs). Although supervised deep learning methods have surpassed traditional methods in performance, their practical applicability is limited by the lack of ground-truth PE labels in real data. To address this issue, we propose an innovative weakly supervised waveform simulation and reconstruction approach based on a bidirectional conditional diffusion network framework. The method is fully data-driven and requires only raw waveforms and coarse estimates of PE information as input. It first employs a PE-conditioned diffusion model to simulate realistic waveforms from PE sequences, thereby learning the features of overlapping waveforms. Subsequently, these simulated waveforms are used to train a waveform-conditioned diffusion model to reconstruct the PE sequences from waveforms, reinforcing the learning of features of overlapping waveforms. Through iterative refinement between the two conditional diffusion processes, the model progressively improves reconstruction accuracy. Experimental results demonstrate that the proposed method achieves 99% of the normalized PE-number resolution averaged over 1-5 p.e. and 80% of the timing resolution attained by fully supervised learning.

翻译：光电倍增管（PMT）广泛应用于粒子与核物理实验中。PMT波形重建的精度直接影响探测器的空间与能量分辨率。一个关键挑战在于，当多个光子在数纳秒内相继到达时，难以分辨单个光电子（PE）。尽管有监督深度学习方法在性能上已超越传统方法，但由于真实数据中缺乏真实的光电子标签，其实际应用受到限制。为解决这一问题，我们提出了一种基于双向条件扩散网络框架的创新性弱监督波形模拟与重建方法。该方法完全由数据驱动，仅需原始波形和粗略的光电子信息估计作为输入。它首先采用一个以光电子为条件的扩散模型，从光电子序列模拟出逼真的波形，从而学习重叠波形的特征。随后，利用这些模拟波形训练一个以波形为条件的扩散模型，从波形重建光电子序列，进一步强化对重叠波形特征的学习。通过两个条件扩散过程之间的迭代优化，模型逐步提高重建精度。实验结果表明，所提方法在1-5个光电子范围内平均实现了全监督学习所能达到的归一化光电子数分辨率的99%以及时间分辨率的80%。