# AdaSTI: Conditional Diffusion Models with Adaptive Dependency Modeling for Spatio-Temporal Imputation

arXiv: https://arxiv.org/abs/2509.18144 · HTML: https://mlsanity.com/paper/2509.18144/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 20 of its 35 references that are in the map.
- First posted on arXiv 15 Sep 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, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (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)
- [Multi-Time Attention Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/2101.10318/) (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)
- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [Tensor Completion for Weakly-dependent Data on Graph for Metro Passenger Flow Prediction](https://mlsanity.com/paper/1912.05693/) (2019)
- [Towards Unifying Diffusion Models for Probabilistic Spatio-Temporal Graph Learning](https://mlsanity.com/paper/2310.17360/) (2023)
- [RDIS: Random Drop Imputation with Self-Training for Incomplete Time Series Data](https://mlsanity.com/paper/2010.10075/) (2020)
- [A Temporally Disentangled Contrastive Diffusion Model for Spatiotemporal Imputation](https://mlsanity.com/paper/2402.11558/) (2024)
- [Signal Decomposition Using Masked Proximal Operators](https://mlsanity.com/paper/2202.09338/) (2022)
- [Networked Time Series Prediction with Incomplete Data via Generative Adversarial Network](https://mlsanity.com/paper/2110.02271/) (2021)

## Abstract (arXiv)

Spatio-temporal data abounds in domain like traffic and environmental monitoring. However, it often suffers from missing values due to sensor malfunctions, transmission failures, etc. Recent years have seen continued efforts to improve spatio-temporal data imputation performance. Recently diffusion models have outperformed other approaches in various tasks, including spatio-temporal imputation, showing competitive performance. Extracting and utilizing spatio-temporal dependencies as conditional information is vital in diffusion-based methods. However, previous methods introduce error accumulation in this process and ignore the variability of the dependencies in the noisy data at different diffusion steps. In this paper, we propose AdaSTI (Adaptive Dependency Model in Diffusion-based Spatio-Temporal Imputation), a novel spatio-temporal imputation approach based on conditional diffusion model. Inside AdaSTI, we propose a BiS4PI network based on a bi-directional S4 model for pre-imputation with the imputed result used to extract conditional information by our designed Spatio-Temporal Conditionalizer (STC)network. We also propose a Noise-Aware Spatio-Temporal (NAST) network with a gated attention mechanism to capture the variant dependencies across diffusion steps. Extensive experiments on three real-world datasets show that AdaSTI outperforms existing methods in all the settings, with up to 46.4% reduction in imputation error.