Diffusion models have taken the machine learning world by storm in recent years, powering everything from photorealistic image generators to medical image reconstruction tools. The core idea is elegant. During training, a model learns to destroy an image step by step, gradually adding random noise until nothing recognizable remains. It then learns to reverse that process, peeling away noise layer by layer until a coherent image emerges. Applied to restoration tasks like dehazing, this generative machinery can reconstruct plausible scene details that were obscured by the atmosphere, rather than merely enhancing whatever faint signals survive the haze. But the Dalian team, led by authors Xinyue Liu, Jiayu Liu, Junchi Wu, Linlin Zong, and Wenxin Liang, identified two major weaknesses that have kept diffusion-based dehazing from reaching its full potential.

The first weakness concerns stability under severe haze. Many existing approaches attempt a coarse-to-fine restoration, first recovering the rough layout of a scene and then progressively refining the details. In theory this is sensible; in practice, when the haze is dense and non-uniform, the transition between the coarse and fine stages can become unstable, producing restoration results that fluctuate wildly or degrade as the process advances. Scene structures that survived the early stages may be lost during the fine refinement, and the model may hallucinate inconsistent details from one iteration to the next. Under thick atmospheric haze, where the input already contains precious little information, this instability is not a cosmetic nuisance. It is the difference between a usable image and a muddled mess.

The second weakness is more subtle but equally damaging: stochastic color inconsistency. Because diffusion models generate images through an iterative, inherently random sampling process, the colors of the final output can drift unpredictably. The resulting images often exhibit color shift artifacts, where the overall tone of the restored scene deviates from what the true scene would look like. A slate-gray road might come out tinted blue, or a neutral wall might take on a warm cast. For applications where color fidelity matters, from surveillance to remote sensing to everyday photography, this stochastic drift undermines trust in the reconstruction. The researchers set out to solve both problems within a single, unified framework.

Their answer to the instability problem is a progressive diffusion framework that gradually increases image resolution during both training and inference. Rather than asking the model to jump from a heavily degraded, low-information input directly to a full-resolution reconstruction, the framework works its way up in stages. At each stage, the model operates at a particular resolution, learning stage-wise features appropriate to that scale before the image is handed to the next, higher-resolution stage. To make this efficient, the team designed a progressive backbone architecture that evolves with the input scale, allowing the network to adapt its internal structure as the resolution climbs. Crucially, they also introduced a fade-in strategy that smoothly transitions the optimization between adjacent restoration stages. Instead of an abrupt switch that can shock the model and destabilize training, the fade-in blends the stages so that the coarse-to-fine progression remains stable even under the harshest haze conditions.

The answer to the color drift problem is a consistency-preserving group-level feature statistics module. During the diffusion sampling process, this module regularizes the consistency of feature distributions, keeping the statistical properties of the internal representations aligned across the many denoising steps. By anchoring these feature statistics, the framework reduces the random color deviations that plague conventional diffusion sampling and improves global color fidelity. In other words, the model is not left to wander freely through the space of plausible colorings as it denoises; it is gently steered to stay true to the color character of the scene it is restoring. The result is a dehazed image whose hues remain where they should be, from the first sampling step to the last.

The evidence for these design choices comes from an extensive battery of experiments on both synthetic and real-world datasets. On the synthetic side, the researchers evaluated PD-Dehaze on the SOTS-Indoor and SOTS-Outdoor benchmarks, standard testbeds for dehazing research. An interesting observation from their results is that, given the relatively mild degradation in the SOTS datasets, most recent methods published since 2022 have achieved near-saturation performance, indicating that thin synthetic haze is comparatively tractable. Even in this crowded, high-performing field, PD-Dehaze held its own. On the SOTS-Indoor dataset it achieved the second-best SSIM, a structural similarity metric that measures how closely the restored image matches the ground truth in structure and texture. On SOTS-Outdoor, it attained the top PSNR result while ranking second in SSIM, demonstrating that even in easier synthetic scenarios the progressive diffusion strategy delivers highly competitive quality and robustness.

Perhaps more telling is how the model performs when it leaves the comfort of synthetic data. To examine generalization, the team deployed PD-Dehaze directly on two real-world hazy image datasets, URHI and RTTS, without any additional fine-tuning. The model had been trained solely on the NH-HAZE dataset, which contains dense and non-uniform haze, and was then released onto genuinely unconstrained conditions. Because real hazy images come with no clean ground truth, the researchers used two widely adopted no-reference image quality metrics, BRISQUE and NIQE, both of which assess perceptual quality without needing a pristine reference. PD-Dehaze consistently achieved better perceptual quality on both datasets, as indicated by lower BRISQUE and NIQE scores, a result the authors say clearly demonstrates the superior generalization capability of their approach. For a field where models trained on synthetic haze often stumble on real fog, that cross-domain transfer is a meaningful achievement.

The team also went to unusual lengths to quantify the color consistency problem itself. They proposed a new metric called C-Diff, short for Color Difference, which computes the pixel-wise color deviation between a restored output and its ground truth. Both images are converted to HSV color space, and the mean squared error is calculated across the hue, saturation, and brightness channels; a lower C-Diff score signals better color consistency and less distortion. In side-by-side comparisons, a model trained without the consistency guidance suffered severe color distortion, particularly in regions with dense textures or illumination changes, and this showed up both in high C-Diff values and in intense HSV error heatmaps. The consistency-preserving model, by contrast, produced outputs visually faithful to the ground truth, with significantly reduced color deviation and improved spatial coherence. The researchers further analyzed the probability distributions of the output images in LAB color space, finding that the distributions of the L, a, and b channels produced by the constrained model align more closely with the ground truth, especially in the b channel, which is particularly sensitive to color shift. Together, these analyses show that the consistency-aware regularization is doing exactly what it was designed to do.

The broader significance of this work lies in what it says about the maturing of diffusion models for image restoration. The technology’s generative power is not in doubt; what has been missing is the engineering discipline to keep that power stable and faithful under real-world stress. PD-Dehaze tackles that discipline on two fronts at once, combining a resolution-climbing architecture with a fade-in optimization schedule to tame the coarse-to-fine instability, and a feature-statistics regularizer to pin down the color. The framework restores scene structures and fine textures while significantly improving perceptual color consistency, achieving highly competitive performance across the evaluated benchmarks. The authors received no specific funding for the work and declare no competing interests, and the code of PD-Dehaze has been made publicly available, inviting other researchers to build on the approach. As diffusion models continue their march through computer vision, techniques like progressive resolution scaling and consistency-preserving sampling are likely to spread well beyond dehazing, into any task where a machine must conjure a clean image from a corrupted one without losing sight of what the original scene actually looked like.

Subject of Research: Diffusion model-based single image dehazing using progressive resolution restoration and color consistency preservation

Article Title: Progressive Diffusion for Single Image Dehazing

Article References: Liu, X., Liu, J., Wu, J., Zong, L., & Liang, W. (2026). Progressive Diffusion for Single Image Dehazing. Neural Processing Letters. https://doi.org/10.1007/s11063-026-11886-7

Image Credits: AI Generated

DOI: 10.1007/s11063-026-11886-7

Keywords: single image dehazing, diffusion model, denoising diffusion probabilistic models, image restoration, progressive reconstruction, color consistency, computer vision, DDPM, deep learning, image quality assessment, color shift artifacts, Neural Processing Letters

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