# Deep Generative Transformers for Probabilistic Time Series and Spatiotemporal Forecasting

arXiv: https://arxiv.org/abs/2603.11909 · HTML: https://mlsanity.com/paper/2603.11909/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 30 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [On The Computational Complexity of Self-Attention](https://mlsanity.com/paper/2209.04881/) (2022)
- [Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement](https://mlsanity.com/paper/2301.03028/) (2023)
- [Engression: Extrapolation through the Lens of Distributional Regression](https://mlsanity.com/paper/2307.00835/) (2023)
- [TACTiS: Transformer-Attentional Copulas for Time Series](https://mlsanity.com/paper/2202.03528/) (2022)
- [MG-TSD: Multi-Granularity Time Series Diffusion Models with Guided Learning Process](https://mlsanity.com/paper/2403.05751/) (2024)
- [Chickenpox Cases in Hungary: a Benchmark Dataset for Spatiotemporal Signal Processing with Graph Neural Networks](https://mlsanity.com/paper/2102.08100/) (2021)
- [Deep Generative Spatiotemporal Engression for Probabilistic Forecasting of Epidemics](https://mlsanity.com/paper/2603.07108/) (2026)

## Abstract (arXiv)

Reliable uncertainty quantification is paramount for forecasting multivariate time series and spatiotemporal data. While Transformer architectures excel at sequence modeling, current probabilistic approaches typically rely on restrictive parametric likelihoods or quantile-based objectives, thereby limiting their ability to capture complex joint distributions in correlated time series. To overcome these limitations, we propose textitEnformer and its spatiotemporal extension, textitGEnformer. These models synthesize the expressive power of Transformers with engression, a stochastic learning paradigm for modeling conditional distributions. By injecting stochastic noise and optimizing a strictly proper scoring objective, our frameworks directly learn conditional predictive distributions without imposing parametric assumptions. This design ensures the generation of coherent multivariate trajectories while maintaining the Transformer's efficacy in modeling long-range dependencies and cross-series interactions. The probabilistic capability of Enformer is achieved with an asymptotic overhead of only a constant factor over a deterministic Transformer with an identical configuration. We extensively evaluate our frameworks on prominent multivariate benchmarks for temporal dynamics and real-world epidemic datasets for spatiotemporal dynamics. Empirical results demonstrate that both frameworks yield calibrated probabilistic forecasts and consistently outperform state-of-the-art baselines.