# Diff-MN: Diffusion Parameterized MoE-NCDE for Continuous Time Series Generation with Irregular Observations

arXiv: https://arxiv.org/abs/2601.13534 · HTML: https://mlsanity.com/paper/2601.13534/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in MoE for time series and graphs, one of 12 directions in Mixture-of-experts.
- Builds on 24 of its 43 references that are in the map.
- First posted on arXiv 20 Jan 2026.

## Placed in

- Mixture-of-experts / [MoE for time series and graphs](https://mlsanity.com/moe/moe-for-time-series-and-graphs/)

## Builds on (most cited first, 24 of 24)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)
- [TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generation](https://mlsanity.com/paper/2111.08095/) (2021)
- [Diffusion Models for Time Series Applications: A Survey](https://mlsanity.com/paper/2305.00624/) (2023)
- [Vector Quantized Time Series Generation with a Bidirectional Prior Model](https://mlsanity.com/paper/2303.04743/) (2023)
- [Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEs](https://mlsanity.com/paper/2310.02619/) (2023)
- [GT-GAN: General Purpose Time Series Synthesis with Generative Adversarial Networks](https://mlsanity.com/paper/2210.02040/) (2022)
- [Modeling Continuous Stochastic Processes with Dynamic Normalizing Flows](https://mlsanity.com/paper/2002.10516/) (2020)
- [T-CGAN: Conditional Generative Adversarial Network for Data Augmentation in Noisy Time Series with Irregular Sampling](https://mlsanity.com/paper/1811.08295/) (2018)
- [Reliable Generation of Privacy-preserving Synthetic Electronic Health Record Time Series via Diffusion Models](https://mlsanity.com/paper/2310.15290/) (2023)
- [MIRA: Medical Time Series Foundation Model for Real-World Health Data](https://mlsanity.com/paper/2506.07584/) (2025)
- [TimeDP: Learning to Generate Multi-Domain Time Series with Domain Prompts](https://mlsanity.com/paper/2501.05403/) (2025)
- [Irregular Traffic Time Series Forecasting Based on Asynchronous Spatio-Temporal Graph Convolutional Network](https://mlsanity.com/paper/2308.16818/) (2023)
- [T2S: High-resolution Time Series Generation with Text-to-Series Diffusion Models](https://mlsanity.com/paper/2505.02417/) (2025)
- [BRIDGE: Bootstrapping Text to Control Time-Series Generation via Multi-Agent Iterative Optimization and Diffusion Modeling](https://mlsanity.com/paper/2503.02445/) (2025)
- [TSGM: A Flexible Framework for Generative Modeling of Synthetic Time Series](https://mlsanity.com/paper/2305.11567/) (2023)
- [Multi-period Learning for Financial Time Series Forecasting](https://mlsanity.com/paper/2511.08622/) (2025)
- [TarDiff: Target-Oriented Diffusion Guidance for Synthetic Electronic Health Record Time Series Generation](https://mlsanity.com/paper/2504.17613/) (2025)
- [Causal Time Series Generation via Diffusion Models](https://mlsanity.com/paper/2509.20846/) (2025)
- [TS-Diffusion: Generating Highly Complex Time Series with Diffusion Models](https://mlsanity.com/paper/2311.03303/) (2023)
- [CENTS: Generating synthetic electricity consumption time series for rare and unseen scenarios](https://mlsanity.com/paper/2501.14426/) (2025)
- [TSGM: Regular and Irregular Time-series Generation using Score-based Generative Models](https://mlsanity.com/paper/2511.21335/) (2025)
- [Volatility and irregularity Capturing in stock price indices using time series Generative adversarial networks (TimeGAN)](https://mlsanity.com/paper/2311.12987/) (2023)

## Built on by (most cited first, 2 of 2)

- [Lost in the Non-convex Loss Landscape: How to Fine-tune the Large Time Series Model?](https://mlsanity.com/paper/2606.08578/) (2026)
- [Self-Adaptive Scale Handling for Forecasting Time Series with Scale Heterogeneity](https://mlsanity.com/paper/2606.20010/) (2026)

## Abstract (arXiv)

Time series generation (TSG) is widely used across domains, yet most existing methods assume regular sampling and fixed output resolutions. These assumptions are often violated in practice, where observations are irregular and sparse, while downstream applications require continuous and high-resolution TS. Although Neural Controlled Differential Equation (NCDE) is promising for modeling irregular TS, it is constrained by a single dynamics function, tightly coupled optimization, and limited ability to adapt learned dynamics to newly generated samples from the generative model. We propose Diff-MN, a continuous TSG framework that enhances NCDE with a Mixture-of-Experts (MoE) dynamics function and a decoupled architectural design for dynamics-focused training. To further enable NCDE to generalize to newly generated samples, Diff-MN employs a diffusion model to parameterize the NCDE temporal dynamics parameters (MoE weights), i.e., jointly learn the distribution of TS data and MoE weights. This design allows sample-specific NCDE parameters to be generated for continuous TS generation. Experiments on ten public and synthetic datasets demonstrate that Diff-MN consistently outperforms strong baselines on both irregular-to-regular and irregular-to-continuous TSG tasks. The code is available at the link https://github.com/microsoft/TimeCraft/tree/main/Diff-MN.