# Unveiling Stochasticity: Universal Multi-modal Probabilistic Modeling for Traffic Forecasting

arXiv: https://arxiv.org/abs/2604.16084 · HTML: https://mlsanity.com/paper/2604.16084/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 65 references that are in the map.
- First posted on arXiv 17 Apr 2026.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [Spatial-Temporal Identity: A Simple yet Effective Baseline for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2208.05233/) (2022)
- [Two-layer adaptive signal control framework for large-scale dynamically-congested networks: Combining efficient Max Pressure with Perimeter Control](https://mlsanity.com/paper/2210.10453/) (2022)
- [HUTFormer: Hierarchical U-Net Transformer for Long-Term Traffic Forecasting](https://mlsanity.com/paper/2307.14596/) (2023)
- [Advanced computer vision for extracting georeferenced vehicle trajectories from drone imagery](https://mlsanity.com/paper/2411.02136/) (2024)
- [Decompositions of the mean continuous ranked probability score](https://mlsanity.com/paper/2311.14122/) (2023)
- [Adaptive Modeling of Uncertainties for Traffic Forecasting](https://mlsanity.com/paper/2303.09273/) (2023)
- [Bayesian Spatio-Temporal Graph Convolutional Network for Traffic Forecasting](https://mlsanity.com/paper/2010.07498/) (2020)
- [A Bayesian approach to quantifying uncertainties and improving generalizability in traffic prediction models](https://mlsanity.com/paper/2307.05946/) (2023)
- [Traffic signal prediction on transportation networks using spatio-temporal correlations on graphs](https://mlsanity.com/paper/2104.13414/) (2021)
- [Multi-Source Urban Traffic Flow Forecasting with Drone and Loop Detector Data](https://mlsanity.com/paper/2501.03492/) (2025)

## Built on by (most cited first, 2 of 2)

- [Metropolis-Scale Resilient and Trustworthy Traffic Flow Inference Using Multi-Source Data](https://mlsanity.com/paper/2605.25004/) (2026)
- [Joint upper-bound coverage and route-choice utility: an empirical evaluation on two urban proxy tasks](https://mlsanity.com/paper/2610.06995/) (2026)

## Abstract (arXiv)

Traffic forecasting is a challenging spatio-temporal modeling task and a critical component of urban transportation management. Current studies mainly focus on deterministic predictions, with limited considerations on the uncertainty and stochasticity in traffic dynamics. Therefore, this paper proposes an elegant yet universal approach that transforms existing models into probabilistic predictors by replacing only the final output layer with a novel Gaussian Mixture Model (GMM) layer. The modified model requires no changes to the training pipeline and can be trained using only the Negative Log-Likelihood (NLL) loss, without any auxiliary or regularization terms. Experiments on multiple traffic datasets show that our approach generalizes from classic to modern model architectures while preserving deterministic performance. Furthermore, we propose a systematic evaluation procedure based on cumulative distributions and confidence intervals, and demonstrate that our approach is considerably more accurate and informative than unimodal or deterministic baselines. Finally, a more detailed study on a real-world dense urban traffic network is presented to examine the impact of data quality on uncertainty quantification and to show the robustness of our approach under imperfect data conditions. Code available at https://github.com/Weijiang-Xiong/OpenSkyTraffic