# ProGen: Revisiting Probabilistic Spatial-Temporal Time Series Forecasting from a Continuous Generative Perspective Using Stochastic Differential Equations

arXiv: https://arxiv.org/abs/2411.01267 · HTML: https://mlsanity.com/paper/2411.01267/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 21 of its 33 references that are in the map.
- First posted on arXiv 2 Nov 2024.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 21 of 21)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Graph Neural Controlled Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2112.03558/) (2021)
- [Patch Diffusion: Faster and More Data-Efficient Training of Diffusion Models](https://mlsanity.com/paper/2304.12526/) (2023)
- [DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models](https://mlsanity.com/paper/2301.13629/) (2023)
- [Quantifying Uncertainty in Deep Spatiotemporal Forecasting](https://mlsanity.com/paper/2105.11982/) (2021)
- [ScoreGrad: Multivariate Probabilistic Time Series Forecasting with Continuous Energy-based Generative Models](https://mlsanity.com/paper/2106.10121/) (2021)
- [Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusion](https://mlsanity.com/paper/2211.02590/) (2022)
- [AST-GCN: Attribute-Augmented Spatiotemporal Graph Convolutional Network for Traffic Forecasting](https://mlsanity.com/paper/2011.11004/) (2020)
- [Graph Neural Rough Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2303.10909/) (2023)
- [Towards Faster Training of Diffusion Models: An Inspiration of A Consistency Phenomenon](https://mlsanity.com/paper/2404.07946/) (2024)

## Abstract (arXiv)

Accurate forecasting of spatiotemporal data remains challenging due to complex spatial dependencies and temporal dynamics. The inherent uncertainty and variability in such data often render deterministic models insufficient, prompting a shift towards probabilistic approaches, where diffusion-based generative models have emerged as effective solutions. In this paper, we present ProGen, a novel framework for probabilistic spatiotemporal time series forecasting that leverages Stochastic Differential Equations (SDEs) and diffusion-based generative modeling techniques in the continuous domain. By integrating a novel denoising score model, graph neural networks, and a tailored SDE, ProGen provides a robust solution that effectively captures spatiotemporal dependencies while managing uncertainty. Our extensive experiments on four benchmark traffic datasets demonstrate that ProGen outperforms state-of-the-art deterministic and probabilistic models. This work contributes a continuous, diffusion-based generative approach to spatiotemporal forecasting, paving the way for future research in probabilistic modeling and stochastic processes.