# From Noise to Laws: Regularized Time-Series Forecasting via Denoised Dynamic Graphs

arXiv: https://arxiv.org/abs/2510.17817 · HTML: https://mlsanity.com/paper/2510.17817/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 34 references that are in the map.
- First posted on arXiv 27 Sep 2025.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [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)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [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)
- [A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction](https://mlsanity.com/paper/1704.02971/) (2017)
- [Less Is More: Fast Multivariate Time Series Forecasting with Light Sampling-oriented MLP Structures](https://mlsanity.com/paper/2207.01186/) (2022)
- [N-HiTS: Neural Hierarchical Interpolation for Time Series Forecasting](https://mlsanity.com/paper/2201.12886/) (2022)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)

## Abstract (arXiv)

Long-horizon multivariate time-series forecasting is challenging because realistic predictions must (i) denoise heterogeneous signals, (ii) track time-varying cross-series dependencies, and (iii) remain stable and physically plausible over long rollout horizons. We present PRISM, which couples a score-based diffusion preconditioner with a dynamic, correlation-thresholded graph encoder and a forecast head regularized by generic physics penalties. We prove contraction of the induced horizon dynamics under mild conditions and derive Lipschitz bounds for graph blocks, explaining the model's robustness. On six standard benchmarks , PRISM achieves consistent SOTA with strong MSE and MAE gains.