Diffusion Transformers for Imputation: Statistical Efficiency and Uncertainty Quantification
On the map: Diffusion models → Flow matching, time series and science
Abstract (arXiv)
Imputation methods play a critical role in enhancing the quality of practical time-series data, which often suffer from pervasive missing values. Recently, diffusion-based generative imputation methods have demonstrated remarkable success compared to autoregressive and conventional statistical approaches. Despite their empirical success, the theoretical understanding of how well diffusion-based models capture complex spatial and temporal dependencies between the missing values and observed ones remains limited. Our work addresses this gap by investigating the statistical efficiency of conditional diffusion transformers for imputation and quantifying the uncertainty in missing values. Specifically, we derive statistical sample complexity bounds based on a novel approximation theory for conditional score functions using transformers, and, through this, construct tight confidence regions for missing values. Our findings also reveal that the efficiency and accuracy of imputation are significantly influenced by the missing patterns. Furthermore, we validate these theoretical insights through simulation and propose a mixed-masking training strategy to enhance the imputation performance.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 38 of its 71 references that are in the map. First posted on arXiv 2 Oct 2025.
Builds on
38 of 71 references.
Closest ancestors · 6
Same direction, newest first
- 2024TimeDiT: General-purpose Diffusion Transformers for Time Series Foundation Model3 Sep
- 2024MTSCI: A Conditional Diffusion Model for Multivariate Time Series Consistent Imputation11 Aug
- 2023MissDiff: Training Diffusion Models on Tabular Data with Missing Values2 Jul
- 2023PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation20 Feb
- 2022Diffusion models for missing value imputation in tabular data31 Oct
- 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation7 Jul
Other references · 32
- 2017Attention Is All You Needcited by 59,932
- 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
- 2022Scalable Diffusion Models with Transformerscited by 5,931
- 2022TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysiscited by 1,030
- 2014Convex Optimization: Algorithms and Complexitycited by 569
- 2016Recurrent Neural Networks for Multivariate Time Series with Missing Valuescited by 548
- 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 440
- 2018GAIN: Missing Data Imputation using Generative Adversarial Netscited by 349
- 2018BRITS: Bidirectional Recurrent Imputation for Time Seriescited by 288
- 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localizationcited by 230
- 2021Unsupervised Representation Learning for Time Series with Temporal Neighborhood Codingcited by 223
- 2022Diffusion-based Time Series Imputation and Forecasting with Structured State Space Modelscited by 195
20 more
- 2019GP-VAE: Deep Probabilistic Time Series Imputationcited by 171
- 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Datacited by 171
- 2022SAITS: Self-Attention-based Imputation for Time Seriescited by 167
- 2023Diffusion Models are Minimax Optimal Distribution Estimatorscited by 159
- 2021Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networkscited by 93
- 2017Estimating Missing Data in Temporal Data Streams Using Multi-directional Recurrent Neural Networkscited by 86
- 2024Accelerating Convergence of Score-Based Diffusion Models, Provablycited by 74
- 2020Mat'ern Gaussian Processes on Graphscited by 65
- 2024Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorialcited by 60
- 2024Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theorycited by 58
- 2024Deep Learning for Multivariate Time Series Imputation: A Surveycited by 57
- 2023Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Modelscited by 39
- 2020Time Series Data Imputation: A Survey on Deep Learning Approachescited by 34
- 2020Uncertainty-Aware Variational-Recurrent Imputation Network for Clinical Time Seriescited by 33
- 2021Missing Value Imputation on Multidimensional Time Seriescited by 33
- 2024TSI-Bench: Benchmarking Time Series Imputationcited by 33
- 2023Deep Imputation of Missing Values in Time Series Health Data: A Review with Benchmarkingcited by 29
- 2023Probabilistic Imputation for Time-series Classification with Missing Datacited by 21
- 2022Missing Data Imputation and Acquisition with Deep Hierarchical Models and Hamiltonian Monte Carlocited by 19
- 2024Diffusion Transformer Captures Spatial-Temporal Dependencies: A Theory for Gaussian Process Datacited by 5
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- 2024Latent Space Score-based Diffusion Model for Probabilistic Multivariate Time Series Imputation
- 2026Discretizing Continuous Time Series for Imputation with Masked Diffusion Training
- 2026Analyzing and Improving Diffusion Models for Time-Series Data Imputation: A Proximal Recursion Perspective
- 2025Cross-Domain Conditional Diffusion Models for Time Series Imputation
- 2025Boundary-enhanced time series data imputation with long-term dependency diffusion models
- 2026RDDMPI: Residual Denoising Diffusion Model for Probabilistic Multivariate Time Series Imputation
- 2025Exploiting the Prior of Generative Time Series Imputation
- 2024DiffPuter: Empowering Diffusion Models for Missing Data Imputation