# STDiff: A State Transition Diffusion Framework for Time Series Imputation in Industrial Systems

arXiv: https://arxiv.org/abs/2508.19011 · HTML: https://mlsanity.com/paper/2508.19011/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 45 of its 83 references that are in the map.
- First posted on arXiv 26 Aug 2025.

## Builds on (most cited first, 30 of 45)

- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [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)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [History-Guided Video Diffusion](https://mlsanity.com/paper/2502.06764/) (2025)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [Score-based Diffusion Models in Function Space](https://mlsanity.com/paper/2302.07400/) (2023)
- [Ca2-VDM: Efficient Autoregressive Video Diffusion Model with Causal Generation and Cache Sharing](https://mlsanity.com/paper/2411.16375/) (2024)

## Abstract (arXiv)

Incomplete sensor data is a major obstacle in industrial time-series analytics. In wastewater treatment plants (WWTPs), key sensors show long, irregular gaps caused by fouling, maintenance, and outages. We introduce STDiff and STDiff-W, diffusion-based imputers that cast gap filling as state-space simulation under partial observability, where targets, controls, and exogenous signals may all be intermittently missing. STDiff learns a one-step transition model conditioned on observed values and masks, while STDiff-W extends this with a context encoder that jointly inpaints contiguous blocks, combining long-range consistency with short-term detail. On two WWTP datasets (one with synthetic block gaps from Agtrup and another with natural outages from Avedore), STDiff-W achieves state-of-the-art accuracy compared with strong neural baselines such as SAITS, BRITS, and CSDI. Beyond point-error metrics, its reconstructions preserve realistic dynamics including oscillations, spikes, and regime shifts, and they achieve top or tied-top downstream one-step forecasting performance compared with strong neural baselines, indicating that preserving dynamics does not come at the expense of predictive utility. Ablation studies that drop, shuffle, or add noise to control or exogenous inputs consistently degrade NH4 and PO4 performance, with the largest deterioration observed when exogenous signals are removed, showing that the model captures meaningful dependencies. We conclude with practical guidance for deployment: evaluate performance beyond MAE using task-oriented and visual checks, include exogenous drivers, and balance computational cost against robustness to structured outages.