# MTSCI: A Conditional Diffusion Model for Multivariate Time Series Consistent Imputation

arXiv: https://arxiv.org/abs/2408.05740 · HTML: https://mlsanity.com/paper/2408.05740/

## Key facts

- Cited by 13 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 22 of its 47 references that are in the map.
- First posted on arXiv 11 Aug 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, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (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)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (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)
- [TS2Vec: Towards Universal Representation of Time Series](https://mlsanity.com/paper/2106.10466/) (2021)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Self-Supervised Contrastive Pre-Training For Time Series via Time-Frequency Consistency](https://mlsanity.com/paper/2206.08496/) (2022)
- [Unsupervised Representation Learning for Time Series with Temporal Neighborhood Coding](https://mlsanity.com/paper/2106.00750/) (2021)
- [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)
- [CoST: Contrastive Learning of Disentangled Seasonal-Trend Representations for Time Series Forecasting](https://mlsanity.com/paper/2202.01575/) (2022)
- [PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation](https://mlsanity.com/paper/2302.09746/) (2023)
- [Joint Air Quality and Weather Prediction Based on Multi-Adversarial Spatiotemporal Networks](https://mlsanity.com/paper/2012.15037/) (2020)
- [MCFlow: Monte Carlo Flow Models for Data Imputation](https://mlsanity.com/paper/2003.12628/) (2020)
- [Learning to Embed Time Series Patches Independently](https://mlsanity.com/paper/2312.16427/) (2023)
- [Neighborhood Contrastive Learning Applied to Online Patient Monitoring](https://mlsanity.com/paper/2106.05142/) (2021)
- [Provably Convergent Schr"odinger Bridge with Applications to Probabilistic Time Series Imputation](https://mlsanity.com/paper/2305.07247/) (2023)

## Built on by (most cited first, 13 of 13)

- [Cross-Domain Conditional Diffusion Models for Time Series Imputation](https://mlsanity.com/paper/2506.12412/) (2025)
- [Boundary-enhanced time series data imputation with long-term dependency diffusion models](https://mlsanity.com/paper/2501.06585/) (2025)
- [FADTI: Fourier and Attention Driven Diffusion for Multivariate Time Series Imputation](https://mlsanity.com/paper/2512.15116/) (2025)
- [A Survey and Benchmarking of Spatial-Temporal Traffic Data Imputation Models](https://mlsanity.com/paper/2412.04733/) (2024)
- [Challenges and Limitations of Generative AI in Synthesizing Wearable Sensor Data](https://mlsanity.com/paper/2505.14206/) (2025)
- [Hallucination Detection and Mitigation with Diffusion in Multi-Variate Time-Series Foundation Models](https://mlsanity.com/paper/2508.00881/) (2025)
- [Semantically-Guided Inference for Conditional Diffusion Models: Enhancing Covariate Consistency in Time Series Forecasting](https://mlsanity.com/paper/2508.01761/) (2025)
- [STDiff: A State Transition Diffusion Framework for Time Series Imputation in Industrial Systems](https://mlsanity.com/paper/2508.19011/) (2025)
- [Diffusion Transformers for Imputation: Statistical Efficiency and Uncertainty Quantification](https://mlsanity.com/paper/2510.02216/) (2025)
- [Missing Pattern Recognized Diffusion Imputation Model for Missing Not At Random](https://mlsanity.com/paper/2605.25439/) (2026)
- [From Coarse to Fine: Managing Temporal Granularity in Spatio-Temporal Data for Fine-Grained Traffic Prediction](https://mlsanity.com/paper/2606.09392/) (2026)
- [RDDMPI: Residual Denoising Diffusion Model for Probabilistic Multivariate Time Series Imputation](https://mlsanity.com/paper/2609.11648/) (2026)
- [ProCTI: Prototype-Refined Global Conditioning for Diffusion-Based Time Series Imputation](https://mlsanity.com/paper/2609.37632/) (2026)

## Abstract (arXiv)

Missing values are prevalent in multivariate time series, compromising the integrity of analyses and degrading the performance of downstream tasks. Consequently, research has focused on multivariate time series imputation, aiming to accurately impute the missing values based on available observations. A key research question is how to ensure imputation consistency, i.e., intra-consistency between observed and imputed values, and inter-consistency between adjacent windows after imputation. However, previous methods rely solely on the inductive bias of the imputation targets to guide the learning process, ignoring imputation consistency and ultimately resulting in poor performance. Diffusion models, known for their powerful generative abilities, prefer to generate consistent results based on available observations. Therefore, we propose a conditional diffusion model for Multivariate Time Series Consistent Imputation (MTSCI). Specifically, MTSCI employs a contrastive complementary mask to generate dual views during the forward noising process. Then, the intra contrastive loss is calculated to ensure intra-consistency between the imputed and observed values. Meanwhile, MTSCI utilizes a mixup mechanism to incorporate conditional information from adjacent windows during the denoising process, facilitating the inter-consistency between imputed samples. Extensive experiments on multiple real-world datasets demonstrate that our method achieves the state-of-the-art performance on multivariate time series imputation task under different missing scenarios. Code is available at https://github.com/JeremyChou28/MTSCI.