# Filling the Missings: Spatiotemporal Data Imputation by Conditional Diffusion

arXiv: https://arxiv.org/abs/2506.07099 · HTML: https://mlsanity.com/paper/2506.07099/

## Key facts

- Cited by 1 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 17 of its 42 references that are in the map.
- First posted on arXiv 8 Jun 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, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [SwiftSage: A Generative Agent with Fast and Slow Thinking for Complex Interactive Tasks](https://mlsanity.com/paper/2305.17390/) (2023)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [GCNet: Graph Completion Network for Incomplete Multimodal Learning in Conversation](https://mlsanity.com/paper/2203.02177/) (2022)
- [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)
- [Uncertainty-Aware Variational-Recurrent Imputation Network for Clinical Time Series](https://mlsanity.com/paper/2003.00662/) (2020)
- [CRPS Learning](https://mlsanity.com/paper/2102.00968/) (2021)
- [FECAM: Frequency Enhanced Channel Attention Mechanism for Time Series Forecasting](https://mlsanity.com/paper/2212.01209/) (2022)
- [Big Learning Expectation Maximization](https://mlsanity.com/paper/2312.11926/) (2023)

## Built on by (most cited first, 1 of 1)

- [Spatiotemporal Imputation with Graph-Informed Flow Matching](https://mlsanity.com/paper/2606.06682/) (2026)

## Abstract (arXiv)

Missing data in spatiotemporal systems presents a significant challenge for modern applications, ranging from environmental monitoring to urban traffic management. The integrity of spatiotemporal data often deteriorates due to hardware malfunctions and software failures in real-world deployments. Current approaches based on machine learning and deep learning struggle to model the intricate interdependencies between spatial and temporal dimensions effectively and, more importantly, suffer from cumulative errors during the data imputation process, which propagate and amplify through iterations. To address these limitations, we propose CoFILL, a novel Conditional Diffusion Model for spatiotemporal data imputation. CoFILL builds on the inherent advantages of diffusion models to generate high-quality imputations without relying on potentially error-prone prior estimates. It incorporates an innovative dual-stream architecture that processes temporal and frequency domain features in parallel. By fusing these complementary features, CoFILL captures both rapid fluctuations and underlying patterns in the data, which enables more robust imputation. The extensive experiments reveal that CoFILL's noise prediction network successfully transforms random noise into meaningful values that align with the true data distribution. The results also show that CoFILL outperforms state-of-the-art methods in imputation accuracy. The source code is publicly available at https://github.com/joyHJL/CoFILL.