# Boundary-enhanced time series data imputation with long-term dependency diffusion models

arXiv: https://arxiv.org/abs/2501.06585 · HTML: https://mlsanity.com/paper/2501.06585/

## 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 29 of its 57 references that are in the map.
- First posted on arXiv 11 Jan 2025.

## 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, 29 of 29)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (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)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [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)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [Long Movie Clip Classification with State-Space Video Models](https://mlsanity.com/paper/2204.01692/) (2022)
- [Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement](https://mlsanity.com/paper/2301.03028/) (2023)
- [Estimating Missing Data in Temporal Data Streams Using Multi-directional Recurrent Neural Networks](https://mlsanity.com/paper/1711.08742/) (2017)
- [Gaussian Process Prior Variational Autoencoders](https://mlsanity.com/paper/1810.11738/) (2018)
- [Diffusion Models for Time Series Applications: A Survey](https://mlsanity.com/paper/2305.00624/) (2023)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
- [NAOMI: Non-Autoregressive Multiresolution Sequence Imputation](https://mlsanity.com/paper/1901.10946/) (2019)
- [Networked Time Series Imputation via Position-aware Graph Enhanced Variational Autoencoders](https://mlsanity.com/paper/2305.18612/) (2023)
- [Leveraging the Exact Likelihood of Deep Latent Variable Models](https://mlsanity.com/paper/1802.04826/) (2018)
- [PC-GAIN: Pseudo-label Conditional Generative Adversarial Imputation Networks for Incomplete Data](https://mlsanity.com/paper/2011.07770/) (2020)
- [MTSCI: A Conditional Diffusion Model for Multivariate Time Series Consistent Imputation](https://mlsanity.com/paper/2408.05740/) (2024)
- [Graph Spatiotemporal Process for Multivariate Time Series Anomaly Detection with Missing Values](https://mlsanity.com/paper/2401.05800/) (2024)
- [Higher-order Spatio-temporal Physics-incorporated Graph Neural Network for Multivariate Time Series Imputation](https://mlsanity.com/paper/2405.10995/) (2024)
- [Counterfactual Data Augmentation with Denoising Diffusion for Graph Anomaly Detection](https://mlsanity.com/paper/2407.02143/) (2024)
- [Avoiding Kernel Fixed Points: Computing with ELU and GELU Infinite Networks](https://mlsanity.com/paper/2002.08517/) (2020)
- [Continuous-time Autoencoders for Regular and Irregular Time Series Imputation](https://mlsanity.com/paper/2312.16581/) (2023)
- [Mining of Switching Sparse Networks for Missing Value Imputation in Multivariate Time Series](https://mlsanity.com/paper/2409.09930/) (2024)
- [Diffusion Model-based Contrastive Learning for Human Activity Recognition](https://mlsanity.com/paper/2408.05567/) (2024)

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

- [Spatial-Temporal Feedback Diffusion Guidance for Controlled Traffic Imputation](https://mlsanity.com/paper/2601.04572/) (2026)
- [CINDI: Conditional Imputation and Noisy Data Integrity with Flows in Power Grid Data](https://mlsanity.com/paper/2603.11745/) (2026)

## Abstract (arXiv)

Data imputation is crucial for addressing challenges posed by missing values in multivariate time series data across various fields, such as healthcare, traffic, and economics, and has garnered significant attention. Among various methods, diffusion model-based approaches show notable performance improvements. However, existing methods often cause disharmonious boundaries between missing and known regions and overlook long-range dependencies in missing data estimation, leading to suboptimal results. To address these issues, we propose a Diffusion-based time Series Data Imputation (DSDI) framework. We develop a weight-reducing injection strategy that incorporates the predicted values of missing points with reducing weights into the reverse diffusion process to mitigate boundary inconsistencies. Further, we introduce a multi-scale S4-based U-Net, which combines hierarchical information from different levels via multi-resolution integration to capture long-term dependencies. Experimental results demonstrate that our model outperforms existing imputation methods.