# FastSTI: A Fast Conditional Pseudo Numerical Diffusion Model for Spatio-temporal Traffic Data Imputation

arXiv: https://arxiv.org/abs/2410.15248 · HTML: https://mlsanity.com/paper/2410.15248/

## Key facts

- Cited by 4 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 23 of its 49 references that are in the map.
- First posted on arXiv 20 Oct 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, 23 of 23)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [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)
- [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)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [Diffusion Models for Time Series Applications: A Survey](https://mlsanity.com/paper/2305.00624/) (2023)
- [PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation](https://mlsanity.com/paper/2302.09746/) (2023)
- [MCFlow: Monte Carlo Flow Models for Data Imputation](https://mlsanity.com/paper/2003.12628/) (2020)
- [Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2104.14936/) (2021)
- [Uncertainty-Aware Variational-Recurrent Imputation Network for Clinical Time Series](https://mlsanity.com/paper/2003.00662/) (2020)
- [AC-VRNN: Attentive Conditional-VRNN for Multi-Future Trajectory Prediction](https://mlsanity.com/paper/2005.08307/) (2020)
- [Spatiotemporal Tensor Completion for Improved Urban Traffic Imputation](https://mlsanity.com/paper/2103.08323/) (2021)

## Built on by (most cited first, 4 of 4)

- [A Survey and Benchmarking of Spatial-Temporal Traffic Data Imputation Models](https://mlsanity.com/paper/2412.04733/) (2024)
- [Neural Canonical Polyadic Factorization for Traffic Analysis](https://mlsanity.com/paper/2506.15079/) (2025)
- [Spectra-Guided Neural Tucker Factorization](https://mlsanity.com/paper/2606.00584/) (2026)
- [A Dataset and Model for Imputing Water Surface Elevation on a Large and Extremely Sparse Spatiotemporal Graph](https://mlsanity.com/paper/2609.11580/) (2026)

## Abstract (arXiv)

High-quality spatiotemporal traffic data is crucial for intelligent transportation systems (ITS) and their data-driven applications. Inevitably, the issue of missing data caused by various disturbances threatens the reliability of data acquisition. Recent studies of diffusion probability models have demonstrated the superiority of deep generative models in imputation tasks by precisely capturing the spatio-temporal correlation of traffic data. One drawback of diffusion models is their slow sampling/denoising process. In this work, we aim to accelerate the imputation process while retaining the performance. We propose a fast conditional diffusion model for spatiotemporal traffic data imputation (FastSTI). To speed up the process yet, obtain better performance, we propose the application of a high-order pseudo-numerical solver. Our method further revs the imputation by introducing a predefined alignment strategy of variance schedule during the sampling process. Evaluating FastSTI on two types of real-world traffic datasets (traffic speed and flow) with different missing data scenarios proves its ability to impute higher-quality samples in only six sampling steps, especially under high missing rates (60% ~ 90%). The experimental results illustrate a speed-up of 8.3 × faster than the current state-of-the-art model while achieving better performance.