# Latent Space Score-based Diffusion Model for Probabilistic Multivariate Time Series Imputation

arXiv: https://arxiv.org/abs/2409.08917 · HTML: https://mlsanity.com/paper/2409.08917/

## Key facts

- Cited by 2 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 18 of its 26 references that are in the map.
- First posted on arXiv 13 Sep 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, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [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)
- [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)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation](https://mlsanity.com/paper/2302.09746/) (2023)
- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [PulseImpute: A Novel Benchmark Task for Pulsative Physiological Signal Imputation](https://mlsanity.com/paper/2212.07514/) (2022)
- [Higher-order Spatio-temporal Physics-incorporated Graph Neural Network for Multivariate Time Series Imputation](https://mlsanity.com/paper/2405.10995/) (2024)
- [Establishing strong imputation performance of a denoising autoencoder in a wide range of missing data problems](https://mlsanity.com/paper/2004.02584/) (2020)
- [Mixed Graph Signal Analysis of Joint Image Denoising / Interpolation](https://mlsanity.com/paper/2309.10114/) (2023)
- [Irregularity-Aware Bandlimited Approximation for Graph Signal Interpolation](https://mlsanity.com/paper/2312.09405/) (2023)

## Built on by (most cited first, 2 of 2)

- [STDiff: A State Transition Diffusion Framework for Time Series Imputation in Industrial Systems](https://mlsanity.com/paper/2508.19011/) (2025)
- [Observation-Aligned Mask Priors for Learning Physical Fields from Authentic Occlusions](https://mlsanity.com/paper/2605.16818/) (2026)

## Abstract (arXiv)

Accurate imputation is essential for the reliability and success of downstream tasks. Recently, diffusion models have attracted great attention in this field. However, these models neglect the latent distribution in a lower-dimensional space derived from the observed data, which limits the generative capacity of the diffusion model. Additionally, dealing with the original missing data without labels becomes particularly problematic. To address these issues, we propose the Latent Space Score-Based Diffusion Model (LSSDM) for probabilistic multivariate time series imputation. Observed values are projected onto low-dimensional latent space and coarse values of the missing data are reconstructed without knowing their ground truth values by this unsupervised learning approach. Finally, the reconstructed values are fed into a conditional diffusion model to obtain the precise imputed values of the time series. In this way, LSSDM not only possesses the power to identify the latent distribution but also seamlessly integrates the diffusion model to obtain the high-fidelity imputed values and assess the uncertainty of the dataset. Experimental results demonstrate that LSSDM achieves superior imputation performance while also providing a better explanation and uncertainty analysis of the imputation mechanism. The website of the code is textithttps://github.com/gorgen2020/LSSDMimputation.