# Deep Learning for Multivariate Time Series Imputation: A Survey

arXiv: https://arxiv.org/abs/2402.04059 · HTML: https://mlsanity.com/paper/2402.04059/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 74 references that are in the map.
- First posted on arXiv 6 Feb 2024.

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [One Fits All:Power General Time Series Analysis by Pretrained LM](https://mlsanity.com/paper/2302.11939/) (2023)
- [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)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Timer: Generative Pre-trained Transformers Are Large Time Series Models](https://mlsanity.com/paper/2402.02368/) (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)
- [Large Models for Time Series and Spatio-Temporal Data: A Survey and Outlook](https://mlsanity.com/paper/2310.10196/) (2023)
- [sktime: A Unified Interface for Machine Learning with Time Series](https://mlsanity.com/paper/1909.07872/) (2019)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [Estimating Missing Data in Temporal Data Streams Using Multi-directional Recurrent Neural Networks](https://mlsanity.com/paper/1711.08742/) (2017)
- [PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation](https://mlsanity.com/paper/2302.09746/) (2023)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
- [MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanisms](https://mlsanity.com/paper/2111.03187/) (2021)
- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusion](https://mlsanity.com/paper/2211.02590/) (2022)
- [Time Series Data Imputation: A Survey on Deep Learning Approaches](https://mlsanity.com/paper/2011.11347/) (2020)
- [Uncertainty-Aware Variational-Recurrent Imputation Network for Clinical Time Series](https://mlsanity.com/paper/2003.00662/) (2020)
- [Missing Value Imputation on Multidimensional Time Series](https://mlsanity.com/paper/2103.01600/) (2021)
- [Provably Convergent Schr"odinger Bridge with Applications to Probabilistic Time Series Imputation](https://mlsanity.com/paper/2305.07247/) (2023)
- [NRTSI: Non-Recurrent Time Series Imputation](https://mlsanity.com/paper/2102.03340/) (2021)

## Built on by (most cited first, 30 of 57)

- [Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts](https://mlsanity.com/paper/2409.16040/) (2024)
- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [TSI-Bench: Benchmarking Time Series Imputation](https://mlsanity.com/paper/2406.12747/) (2024)
- [Foundation Models for Time Series: A Survey](https://mlsanity.com/paper/2504.04011/) (2025)
- [Time-IMM: A Dataset and Benchmark for Irregular Multimodal Multivariate Time Series](https://mlsanity.com/paper/2506.10412/) (2025)
- [Zero-shot Imputation with Foundation Inference Models for Dynamical Systems](https://mlsanity.com/paper/2402.07594/) (2024)
- [BEDTime: A Unified Benchmark for Automatically Describing Time Series](https://mlsanity.com/paper/2509.05215/) (2025)
- [Causality-Aware Spatiotemporal Graph Neural Networks for Spatiotemporal Time Series Imputation](https://mlsanity.com/paper/2403.11960/) (2024)
- [TSAQA: Time Series Analysis Question And Answering Benchmark](https://mlsanity.com/paper/2601.23204/) (2026)
- [TimeCHEAT: A Channel Harmony Strategy for Irregularly Sampled Multivariate Time Series Analysis](https://mlsanity.com/paper/2412.12886/) (2024)
- [Glocal Information Bottleneck for Time Series Imputation](https://mlsanity.com/paper/2510.04910/) (2025)
- [Beyond Random Missingness: Clinically Rethinking for Healthcare Time Series Imputation](https://mlsanity.com/paper/2405.17508/) (2024)
- [Task-oriented Time Series Imputation Evaluation via Generalized Representers](https://mlsanity.com/paper/2410.06652/) (2024)
- [How Deep is your Guess? A Fresh Perspective on Deep Learning for Medical Time-Series Imputation](https://mlsanity.com/paper/2407.08442/) (2024)
- [A Temporally Disentangled Contrastive Diffusion Model for Spatiotemporal Imputation](https://mlsanity.com/paper/2402.11558/) (2024)
- [NuwaTS: a Foundation Model Mending Every Incomplete Time Series](https://mlsanity.com/paper/2405.15317/) (2024)
- [Rethinking the Diffusion Models for Numerical Tabular Data Imputation from the Perspective of Wasserstein Gradient Flow](https://mlsanity.com/paper/2406.15762/) (2024)
- [Using matrix-product states for time-series machine learning](https://mlsanity.com/paper/2412.15826/) (2024)
- [Bridging Smart Meter Gaps: A Benchmark of Statistical, Machine Learning and Time Series Foundation Models for Data Imputation](https://mlsanity.com/paper/2501.07276/) (2025)
- [IMTS is Worth Time × Channel Patches: Visual Masked Autoencoders for Irregular Multivariate Time Series Prediction](https://mlsanity.com/paper/2505.22815/) (2025)
- [MoGU: Mixture-of-Gaussians with Uncertainty-based Gating for Time Series Forecasting](https://mlsanity.com/paper/2510.07459/) (2025)
- [FADTI: Fourier and Attention Driven Diffusion for Multivariate Time Series Imputation](https://mlsanity.com/paper/2512.15116/) (2025)
- [Learning to Factorize and Adapt: A Versatile Approach Toward Universal Spatio-Temporal Foundation Models](https://mlsanity.com/paper/2601.12083/) (2026)
- [Multi-scale hypergraph meets LLMs: Aligning large language models for time series analysis](https://mlsanity.com/paper/2602.04369/) (2026)
- [T1: One-to-One Channel-Head Binding for Multivariate Time-Series Imputation](https://mlsanity.com/paper/2602.21043/) (2026)
- [AION: Next-Generation Tasks and Practical Harness for Time Series](https://mlsanity.com/paper/2605.25045/) (2026)
- [TRACE: A Temporal Conditional Estimation for Multimodal Time Series Foundation Models](https://mlsanity.com/paper/2606.06285/) (2026)
- [TIMBA: Time series Imputation with Bi-directional Mamba Blocks and Diffusion models](https://mlsanity.com/paper/2410.05916/) (2024)
- [Integrating Sequence and Image Modeling in Irregular Medical Time Series Through Self-Supervised Learning](https://mlsanity.com/paper/2502.06134/) (2025)

## Abstract (arXiv)

Missing values are ubiquitous in multivariate time series (MTS) data, posing significant challenges for accurate analysis and downstream applications. In recent years, deep learning-based methods have successfully handled missing data by leveraging complex temporal dependencies and learned data distributions. In this survey, we provide a comprehensive summary of deep learning approaches for multivariate time series imputation (MTSI) tasks. We propose a novel taxonomy that categorizes existing methods based on two key perspectives: imputation uncertainty and neural network architecture. Furthermore, we summarize existing MTSI toolkits with a particular emphasis on the PyPOTS Ecosystem, which provides an integrated and standardized foundation for MTSI research. Finally, we discuss key challenges and future research directions, which give insight for further MTSI research. This survey aims to serve as a valuable resource for researchers and practitioners in the field of time series analysis and missing data imputation tasks.A well-maintained MTSI paper and tool list are available at https://github.com/WenjieDu/Awesome_Imputation.