# NAOMI: Non-Autoregressive Multiresolution Sequence Imputation

arXiv: https://arxiv.org/abs/1901.10946 · HTML: https://mlsanity.com/paper/1901.10946/

## Key facts

- Cited by 59 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2019.

## Built on by (most cited first, 30 of 59)

- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [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)
- [Uncovering the Missing Pattern: Unified Framework Towards Trajectory Imputation and Prediction](https://mlsanity.com/paper/2303.16005/) (2023)
- [Missing Value Imputation on Multidimensional Time Series](https://mlsanity.com/paper/2103.01600/) (2021)
- [Deep Imputation of Missing Values in Time Series Health Data: A Review with Benchmarking](https://mlsanity.com/paper/2302.10902/) (2023)
- [NRTSI: Non-Recurrent Time Series Imputation](https://mlsanity.com/paper/2102.03340/) (2021)
- [Time Series Continuous Modeling for Imputation and Forecasting with Implicit Neural Representations](https://mlsanity.com/paper/2306.05880/) (2023)
- [Unified Uncertainty-Aware Diffusion for Multi-Agent Trajectory Modeling](https://mlsanity.com/paper/2503.18589/) (2025)
- [Ball Trajectory Inference from Multi-Agent Sports Contexts Using Set Transformer and Hierarchical Bi-LSTM](https://mlsanity.com/paper/2306.08206/) (2023)
- [Causality-Aware Spatiotemporal Graph Neural Networks for Spatiotemporal Time Series Imputation](https://mlsanity.com/paper/2403.11960/) (2024)
- [TranSPORTmer: A Holistic Approach to Trajectory Understanding in Multi-Agent Sports](https://mlsanity.com/paper/2410.17785/) (2024)
- [Joint Sensing, Communication, and AI: A Trifecta for Resilient THz User Experiences](https://mlsanity.com/paper/2305.00135/) (2023)
- [BayOTIDE: Bayesian Online Multivariate Time series Imputation with functional decomposition](https://mlsanity.com/paper/2308.14906/) (2023)
- [Forecasting Unobserved Node States with spatio-temporal Graph Neural Networks](https://mlsanity.com/paper/2211.11596/) (2022)
- [PulseImpute: A Novel Benchmark Task for Pulsative Physiological Signal Imputation](https://mlsanity.com/paper/2212.07514/) (2022)
- [Pedestrian Trajectory Prediction with Missing Data: Datasets, Imputation, and Benchmarking](https://mlsanity.com/paper/2411.00174/) (2024)
- [Time-series Imputation of Temporally-occluded Multiagent Trajectories](https://mlsanity.com/paper/2106.04219/) (2021)
- [Taming the Long Tail of Deep Probabilistic Forecasting](https://mlsanity.com/paper/2202.13418/) (2022)
- [Improving Diffusion Models for ECG Imputation with an Augmented Template Prior](https://mlsanity.com/paper/2310.15742/) (2023)
- [Missing Value Imputation for Multi-attribute Sensor Data Streams via Message Propagation (Extended Version)](https://mlsanity.com/paper/2311.07344/) (2023)
- [Data-driven Analysis for Understanding Team Sports Behaviors](https://mlsanity.com/paper/2102.07545/) (2021)
- [EgoTraj-Bench: Towards Robust Trajectory Prediction Under Ego-view Noisy Observations](https://mlsanity.com/paper/2510.00405/) (2025)
- [Deep Neural Imputation: A Framework for Recovering Incomplete Brain Recordings](https://mlsanity.com/paper/2206.08094/) (2022)
- [T2FPV: Dataset and Method for Correcting First-Person View Errors in Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2209.11294/) (2022)
- [How Deep is your Guess? A Fresh Perspective on Deep Learning for Medical Time-Series Imputation](https://mlsanity.com/paper/2407.08442/) (2024)
- [Self-attention-based Diffusion Model for Time-series Imputation in Partial Blackout Scenarios](https://mlsanity.com/paper/2503.01737/) (2025)

## Abstract (arXiv)

Missing value imputation is a fundamental problem in spatiotemporal modeling, from motion tracking to the dynamics of physical systems. Deep autoregressive models suffer from error propagation which becomes catastrophic for imputing long-range sequences. In this paper, we take a non-autoregressive approach and propose a novel deep generative model: Non-AutOregressive Multiresolution Imputation (NAOMI) to impute long-range sequences given arbitrary missing patterns. NAOMI exploits the multiresolution structure of spatiotemporal data and decodes recursively from coarse to fine-grained resolutions using a divide-and-conquer strategy. We further enhance our model with adversarial training. When evaluated extensively on benchmark datasets from systems of both deterministic and stochastic dynamics. NAOMI demonstrates significant improvement in imputation accuracy (reducing average prediction error by 60% compared to autoregressive counterparts) and generalization for long range sequences.