# sasdim: self-adaptive noise scaling diffusion model for spatial time series imputation

arXiv: https://arxiv.org/abs/2309.01988 · HTML: https://mlsanity.com/paper/2309.01988/

## Key facts

- Cited by 7 papers in the map (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 34 references that are in the map.
- First posted on arXiv 5 Sep 2023.

## 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)

- [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)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Deep Learning for Spatio-Temporal Data Mining: A Survey](https://mlsanity.com/paper/1906.04928/) (2019)
- [It's Raw! Audio Generation with State-Space Models](https://mlsanity.com/paper/2202.09729/) (2022)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [What Makes Convolutional Models Great on Long Sequence Modeling?](https://mlsanity.com/paper/2210.09298/) (2022)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)

## Built on by (most cited first, 7 of 7)

- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [Unraveling Spatio-Temporal Foundation Models via the Pipeline Lens: A Comprehensive Review](https://mlsanity.com/paper/2506.01364/) (2025)
- [Anomaly Detection and Generation with Diffusion Models: A Survey](https://mlsanity.com/paper/2506.09368/) (2025)
- [A Survey of Generative AI for Intelligent Transportation Systems: Road Transportation Perspective](https://mlsanity.com/paper/2312.08248/) (2023)
- [FreshRetailNet-50K: A Stockout-Annotated Censored Demand Dataset for Latent Demand Recovery and Forecasting in Fresh Retail](https://mlsanity.com/paper/2505.16319/) (2025)
- [Spatial Imputation Drives Cross-Domain Alignment for EEG Classification](https://mlsanity.com/paper/2508.03437/) (2025)
- [EMAG: Differentiable 4D Gaussian Mixture Splatting for EEG Spatial Super-Resolution](https://mlsanity.com/paper/2605.29731/) (2026)

## Abstract (arXiv)

Spatial time series imputation is critically important to many real applications such as intelligent transportation and air quality monitoring. Although recent transformer and diffusion model based approaches have achieved significant performance gains compared with conventional statistic based methods, spatial time series imputation still remains as a challenging issue due to the complex spatio-temporal dependencies and the noise uncertainty of the spatial time series data. Especially, recent diffusion process based models may introduce random noise to the imputations, and thus cause negative impact on the model performance. To this end, we propose a self-adaptive noise scaling diffusion model named SaSDim to more effectively perform spatial time series imputation. Specially, we propose a new loss function that can scale the noise to the similar intensity, and propose the across spatial-temporal global convolution module to more effectively capture the dynamic spatial-temporal dependencies. Extensive experiments conducted on three real world datasets verify the effectiveness of SaSDim by comparison with current state-of-the-art baselines.