# MoTM: Towards a Foundation Model for Time Series Imputation based on Continuous Modeling

arXiv: https://arxiv.org/abs/2507.13207 · HTML: https://mlsanity.com/paper/2507.13207/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 27 references that are in the map.
- First posted on arXiv 17 Jul 2025.

## Builds on (most cited first, 20 of 20)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [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)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [NAOMI: Non-Autoregressive Multiresolution Sequence Imputation](https://mlsanity.com/paper/1901.10946/) (2019)
- [Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusion](https://mlsanity.com/paper/2211.02590/) (2022)
- [Learning Deep Time-index Models for Time Series Forecasting](https://mlsanity.com/paper/2207.06046/) (2022)
- [Time Series Continuous Modeling for Imputation and Forecasting with Implicit Neural Representations](https://mlsanity.com/paper/2306.05880/) (2023)
- [Time series forecasting with Gaussian Processes needs priors](https://mlsanity.com/paper/2009.08102/) (2020)
- [NuwaTS: a Foundation Model Mending Every Incomplete Time Series](https://mlsanity.com/paper/2405.15317/) (2024)
- [ImputeINR: Time Series Imputation via Implicit Neural Representations for Disease Diagnosis with Missing Data](https://mlsanity.com/paper/2505.10856/) (2025)

## Built on by (most cited first, 1 of 1)

- [Are Time-Indexed Foundation Models the Future of Time Series Imputation?](https://mlsanity.com/paper/2511.05980/) (2025)

## Abstract (arXiv)

Recent years have witnessed a growing interest for time series foundation models, with a strong emphasis on the forecasting task. Yet, the crucial task of out-of-domain imputation of missing values remains largely underexplored. We propose a first step to fill this gap by leveraging implicit neural representations (INRs). INRs model time series as continuous functions and naturally handle various missing data scenarios and sampling rates. While they have shown strong performance within specific distributions, they struggle under distribution shifts. To address this, we introduce MoTM (Mixture of Timeflow Models), a step toward a foundation model for time series imputation. Building on the idea that a new time series is a mixture of previously seen patterns, MoTM combines a basis of INRs, each trained independently on a distinct family of time series, with a ridge regressor that adapts to the observed context at inference. We demonstrate robust in-domain and out-of-domain generalization across diverse imputation scenarios (e.g., block and pointwise missingness, variable sampling rates), paving the way for adaptable foundation imputation models.