# SSD-TS: Exploring the Potential of Linear State Space Models for Diffusion Models in Time Series Imputation

arXiv: https://arxiv.org/abs/2410.13338 · HTML: https://mlsanity.com/paper/2410.13338/

## Key facts

- Cited by 18 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 40 of its 83 references that are in the map.
- First posted on arXiv 17 Oct 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, 30 of 40)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [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)
- [Temporal Convolutional Networks for Action Segmentation and Detection](https://mlsanity.com/paper/1611.05267/) (2016)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods](https://mlsanity.com/paper/2403.20150/) (2024)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Neural Rough Differential Equations for Long Time Series](https://mlsanity.com/paper/2009.08295/) (2020)
- [TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generation](https://mlsanity.com/paper/2111.08095/) (2021)
- [Is Mamba Effective for Time Series Forecasting?](https://mlsanity.com/paper/2403.11144/) (2024)
- [CATCH: Channel-Aware multivariate Time Series Anomaly Detection via Frequency Patching](https://mlsanity.com/paper/2410.12261/) (2024)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
- [Triformer: Triangular, Variable-Specific Attentions for Long Sequence Multivariate Time Series Forecasting--Full Version](https://mlsanity.com/paper/2204.13767/) (2022)
- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [Anomaly Detection of Time Series with Smoothness-Inducing Sequential Variational Auto-Encoder](https://mlsanity.com/paper/2102.01331/) (2021)

## Built on by (most cited first, 18 of 18)

- [Rethinking Irregular Time Series Forecasting: A Simple yet Effective Baseline](https://mlsanity.com/paper/2505.11250/) (2025)
- [Follow-Your-Shape: Shape-Aware Image Editing via Trajectory-Guided Region Control](https://mlsanity.com/paper/2508.08134/) (2025)
- [Bridging Time and Frequency: A Joint Modeling Framework for Irregular Multivariate Time Series Forecasting](https://mlsanity.com/paper/2602.00582/) (2026)
- [K2VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2505.23017/) (2025)
- [Cross-Domain Conditional Diffusion Models for Time Series Imputation](https://mlsanity.com/paper/2506.12412/) (2025)
- [Task-Aware Mixture-of-Experts for Time Series Analysis](https://mlsanity.com/paper/2509.22279/) (2025)
- [FADTI: Fourier and Attention Driven Diffusion for Multivariate Time Series Imputation](https://mlsanity.com/paper/2512.15116/) (2025)
- [Net-Ev2: A Generative Simulator for Network Event Evolution](https://mlsanity.com/paper/2606.12494/) (2026)
- [Segregation and Context Aggregation Network for Real-time Cloud Segmentation](https://mlsanity.com/paper/2504.14178/) (2025)
- [FADE: Adversarial Concept Erasure in Flow Models](https://mlsanity.com/paper/2507.12283/) (2025)
- [GeoMAE: Masking Representation Learning for Spatio-Temporal Graph Forecasting with Missing Values](https://mlsanity.com/paper/2508.14083/) (2025)
- [Robust Concept Erasure in Diffusion Models: A Theoretical Perspective on Security and Robustness](https://mlsanity.com/paper/2509.12024/) (2025)
- [PSMamba: Progressive Self-supervised Vision Mamba for Plant Disease Recognition](https://mlsanity.com/paper/2512.14309/) (2025)
- [TimeGMM: Single-Pass Probabilistic Forecasting via Adaptive Gaussian Mixture Models with Reversible Normalization](https://mlsanity.com/paper/2601.12288/) (2026)
- [Deep Time-Series Forecasting in 10 Years: A Survey](https://mlsanity.com/paper/2603.19899/) (2026)
- [Beyond Static Uncertainty: Modeling Temporal Uncertainty Dynamics for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2603.24254/) (2026)
- [TGSD: Topology-Guided State-Space Diffusion Framework for EEG Spatial Super-Resolution](https://mlsanity.com/paper/2606.03998/) (2026)
- [Disentangling Multi-View Scanning in Mamba for Network Traffic Anomaly Detection](https://mlsanity.com/paper/2607.22829/) (2026)

## Abstract (arXiv)

Probabilistic time series imputation has been widely applied in real-world scenarios due to its ability for uncertainty estimation and denoising diffusion probabilistic models~(DDPMs) have achieved great success in probabilistic time series imputation tasks with its power to model complex distributions. However, current DDPM-based probabilistic time series imputation methodologies are confronted with two types of challenges: 1)textitThe backbone modules of the denoising parts are not capable of achieving sequence modeling with low time complexity. 2)~textitThe architecture of denoising modules can not handle the dependencies in the time series data effectively. To address the first challenge, we explore the potential of state space model, namely Mamba, as the backbone denoising module for DDPMs. To tackle the second challenge, we carefully devise several SSM-based blocks for time series data modeling. Experimental results demonstrate that our approach can achieve state-of-the-art time series imputation results on multiple real-world datasets. Our datasets and code are available at hrefhttps://github.com/decisionintelligence/SSD-TS/https://github.com/decisionintelligence/SSD-TS/