AI Diffusion Network Learns to Read Faint Light Pulses From Neutrino Detectors

Deep beneath the mountains of southern China, and in the icy waters of the Mediterranean and the Pacific, some of the most sensitive particle detectors ever built are listening for the faintest flashes of light in the universe. When a neutrino collides with matter inside a detector like the Jiangmen Underground Neutrino Observatory, or JUNO, it produces a burst of scintillation light that is converted into electrical pulses by thousands of photomultiplier tubes, or PMTs. Reading those pulses accurately is one of the quiet but decisive challenges of modern particle physics, because the precision with which scientists can count individual photons and time their arrivals directly determines how well they can reconstruct the energy and position of the original particle interaction. A new study published in The European Physical Journal C now shows that a generative artificial intelligence technique borrowed from image synthesis can perform this delicate task almost as well as methods that require perfect training labels, opening a practical path for experiments that cannot obtain such labels from real data.

The core difficulty is one of crowding. Each photon that strikes a PMT’s photocathode ejects a single photoelectron, which is amplified into a characteristic pulse lasting tens of nanoseconds. When photons arrive within a few nanoseconds of one another, their pulses pile up into a single tangled waveform, and disentangling how many photoelectrons contributed becomes genuinely hard. Traditional approaches rely on waveform fitting or deconvolution: matching observed signals against expected templates, or mathematically inverting the detector’s response function to recover the underlying signal. These methods, used by experiments such as IceCube and Daya Bay, work well when photons are sparse, but their performance degrades markedly when multiple photoelectrons overlap, and they depend heavily on accurate prior knowledge of how the detector responds.

Machine learning has recently offered a powerful alternative. Supervised convolutional neural networks, trained on simulated waveforms with known photoelectron content, have been shown to improve the energy resolution of liquid scintillator detectors like JUNO by roughly two to three percent. But there is a catch that has limited their real-world impact: supervised learning requires ground-truth labels, meaning the exact number and arrival times of the photoelectrons underlying each waveform. In Monte Carlo simulations, such labels come for free. In real detector data, they simply do not exist. Calibration sources such as lasers and gamma emitters can provide approximate information, but nothing approaching the precision of simulation truth. This gap between what works in simulation and what is possible with real data has been a persistent obstacle for the field.

A team of researchers at Wuyi University in Jiangmen, China, led by Kainan Liu, Jingyu Huang, Guihong Huang and Jianyi Luo, has now proposed an ingenious workaround built on denoising diffusion probabilistic models, the same class of generative networks that powers modern text-to-image systems. Their framework, called a bidirectional conditional diffusion network, consists of two diffusion models that work as a pair. The first, Diffusion-A, is conditioned on a photoelectron sequence and learns to generate realistic PMT waveforms from it. The second, Diffusion-B, is conditioned on a waveform and learns to reconstruct the photoelectron sequence that produced it. Because each model’s output can serve as training material for the other, the two networks can bootstrap each other toward ever better performance, starting from only raw waveforms and coarse, imperfect estimates of the photoelectron content.

The architecture underlying each model is a modified U-Net adapted for one-dimensional waveform data. The condition vector, which encodes the number of photoelectrons in each of a thousand time bins, is mapped through a fully connected layer and fused with the convolutional features, while the diffusion time step is encoded through sinusoidal positional embeddings and injected into every residual block. Group normalization replaces batch normalization for training stability, the Swish activation improves gradient flow, and attention modules at coarser resolutions allow the network to capture long-range temporal dependencies in the waveform. The diffusion process itself runs over 200 steps, with carefully tuned noise schedules: a broad range for the waveform generator, which must recover both the overall envelope and fine temporal structure, and a narrower range for the reconstruction model, which must focus on precisely identifying photoelectron features within noisy sequences.

To train and evaluate the framework, the researchers built an electronics Monte Carlo simulation that reproduces the key characteristics of PMT waveforms in liquid scintillator detectors, drawing on measured pulse shapes from the Daya Bay experiment and parameters inspired by JUNO’s microchannel plate PMTs, including a transit-time spread of eight nanoseconds. They generated four datasets of one million training waveforms each, spanning scenarios from idealized conditions with widely separated photoelectrons to realistic physical events with Poisson-distributed multiplicities and severe overlap. The simulations modeled every ingredient that shapes a real waveform: the scintillation time distribution, the single-photoelectron pulse with its main peak, overshoot and reflection peaks, the charge spectrum with its 0.3 photoelectron-equivalent resolution, and white electronic noise with a standard deviation of 0.7 millivolts, all digitized at one gigahertz with ten-bit precision.

Under fully supervised conditions, where the networks had access to perfect Monte Carlo truth, the results were striking. The waveform generator reproduced single-photoelectron waveforms and charge spectra with deviations below two percent, and captured the statistics of overlapping multi-photoelectron waveforms with charge linearity and resolution consistent with the ideal simulation. The reconstruction model, in turn, recovered photoelectron counts with biases below three percent for up to seven photoelectrons, and achieved timing resolutions better than half a nanosecond, outperforming simple charge-based estimates particularly in the low-multiplicity regime where neutrino physics is most demanding. A ResNet50 classifier trained under identical conditions performed comparably on the counting task, confirming that diffusion networks are well suited to this problem.

The real breakthrough, however, came in the weakly supervised setting. Here the researchers began with only raw waveforms and crude initial photoelectron estimates obtained through a pipeline of bilateral filtering, peak finding and careful selection criteria that discarded severely overlapping signals. Training the reconstruction model directly on these rough labels produced poor results, because the initial waveforms contained almost no photon pile-up and taught the network nothing about overlap. But the iterative refinement changed everything. After the first round of mutual training between the two diffusion models, reconstruction improved substantially; a second iteration brought further gains, and performance converged after roughly five iterations. The mechanism is elegant: the generator learns to synthesize realistic overlapping waveforms, which then teach the reconstruction model to untangle them, and the improved reconstructions in turn refine the generator’s training labels.

The final numbers tell a compelling story. Training on waveforms with an average intensity of about 0.1 photoelectrons, a regime that provides enough clean single-photoelectron pulses to characterize the detector response while including mild overlap without the severe pile-up that corrupts initial labels, the weakly supervised method achieved an average normalized photoelectron-number resolution of 0.18 photoelectrons over the one-to-five photoelectron range, only about one percent worse than fully supervised learning. Its timing resolution of 0.5 nanoseconds was about 25 percent worse than the supervised ceiling, and all weakly supervised models showed a small systematic bias of 0.1 to 0.3 nanoseconds, but both metrics comfortably outperformed a deconvolution method optimized following the Daya Bay scheme, which suffered from missed photoelectrons at higher multiplicities and inherently limited timing precision.

The implications reach well beyond a single detector. Neutrino experiments around the world, from JUNO’s quest to determine the neutrino mass ordering to Hyper-Kamiokande’s pursuit of CP violation and KM3NeT’s hunt for astrophysical neutrinos, all depend on extracting maximal information from PMT waveforms. A method that needs no ground-truth labels, only raw data and coarse calibration estimates, could be applied directly to real detector data, closing the gap between simulation-era promise and operational reality. The authors note that the accuracy of the initial photoelectron estimates remains the critical factor governing performance, and they plan to optimize the network architecture further and extend the approach to vertex and energy reconstruction. But the demonstration that two diffusion models can teach each other to decode the flickering light of a neutrino detector marks a genuinely new chapter in the intersection of generative AI and experimental particle physics, one that may quietly sharpen every future measurement of the universe’s most elusive particles.

Subject of Research: Weakly supervised deep learning for PMT waveform simulation and reconstruction in neutrino detectors

Article Title: Pmt waveform simulation and reconstruction with conditional diffusion network

Article References: Liu, K., Huang, J., Huang, G., & Luo, J. (2026). Pmt waveform simulation and reconstruction with conditional diffusion network. The European Physical Journal C, 86(9), Article 1132. https://doi.org/10.1140/epjc/s10052-026-16415-3

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16415-3

Keywords: photomultiplier tubes, diffusion models, neutrino detectors, JUNO, waveform reconstruction, machine learning, weakly supervised learning, liquid scintillator, particle physics, generative AI, photoelectron counting, denoising diffusion probabilistic models