用双扩散模型提升城市传感网络预测速度与精度，同时保持可信不确定性。
Double-Diffusion: Balancing Speed, Accuracy, and Uncertainty in Probabilistic Forecasting for Urban Sensor Networks
- 引入图热先验作为无参数低通滤波，指导扩散过程起始点。
- 在4个真实空气质量与交通数据集上，概率预测误差最低，采样成本仅为传统方法的几分之一。
- 适合需要快速更新、高置信度预测的城市智能系统开发者使用。
城市传感器网络需要既准确又具备可用不确定性的快速预测，以响应新数据。但这些目标存在冲突：确定性模型不提供分布信息，而扩散模型虽能建模不确定性，却需多步去噪从纯噪声中生成。本文提出双扩散（Double-Diffusion），将封闭形式的图-热先验融入去噪扩散模型。该先验为传感器图上的无参数低通预测，兼具双重作用：作为模型生成的残差目标，同时作为去噪器的条件。反向过程由此从先验附近开始，仅需短时间步去噪，而非从纯噪声合成；名称即体现图扩散与去噪扩散的组合。采用紧凑型去噪器DD-Net，在Resfusion冷启动设定下训练为去噪扩散概率模型（DDPM），生成过程基于先验残差进行短链优化，而非从零合成。通过先验残差的图谱读出，可由训练数据自动学习空间滤波器。在四个真实世界空气质量和交通网络数据集上，双扩散在所有概率方法中均取得最优连续分级评分（CRPS），且点预测精度媲美最强基线，采样成本仅为从噪声出发的扩散方法的极小部分。代码已开源：https://github.com/teddyicare/Double-Diffusion
原文摘要 · Abstract (English)
Urban sensor networks need forecasts that are accurate, carry useful uncertainty, and refresh fast enough to act on as new readings arrive. These goals conflict: deterministic models give no distribution, while diffusion forecasters model uncertainty but denoise from pure noise over many steps. We present Double-Diffusion, which integrates a closed-form graph-heat prior into a denoising diffusion model. The prior is a parameter-free low-pass forecast over the sensor graph, and it serves two roles: it is the residual target the model generates, and it conditions the denoiser. The reverse process therefore starts near the prior and denoises a short warm-started chain instead of synthesizing from pure noise; the name denotes this composition, a graph diffusion feeding a denoising diffusion. A compact denoiser, DD-Net, is trained as a Denoising Diffusion Probabilistic Model (DDPM) in the Resfusion warm-start formulation, so generation refines the prior over a short truncated chain rather than synthesizing from pure noise; a graph-spectral read-out of the prior residual sets its switchable spatial filter per domain from training data alone. On four real-world air quality and traffic networks, Double-Diffusion attains the best CRPS of all probabilistic methods on every dataset and stays competitive in point accuracy with the strongest baselines, at a fraction of the sampling cost of from-noise diffusion. The code is available at: https://github.com/teddyicare/Double-Diffusion
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