# Neural SDEs as a Unified Approach to Continuous-Domain Sequence Modeling

arXiv: https://arxiv.org/abs/2501.18871 · HTML: https://mlsanity.com/paper/2501.18871/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2025.

## Built on by (most cited first, 6 of 6)

- [Deep Neural Networks Inspired by Differential Equations](https://mlsanity.com/paper/2510.09685/) (2025)
- [Robust Filter Attention: Self-Attention as Precision-Weighted State Estimation](https://mlsanity.com/paper/2509.04154/) (2025)
- [Oscillators Are All You Need: Irregular Time Series Modelling via Damped Harmonic Oscillators with Closed-Form Solutions](https://mlsanity.com/paper/2602.12139/) (2026)
- [Dynamical Systems Theory Behind a Hierarchical Reasoning Model](https://mlsanity.com/paper/2603.22871/) (2026)
- [Martingale Neural Operators: Learning Stochastic Marginals via Doob-Meyer Factorization](https://mlsanity.com/paper/2605.15806/) (2026)
- [Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise](https://mlsanity.com/paper/2607.19173/) (2026)

## Abstract (arXiv)

Inspired by the ubiquitous use of differential equations to model continuous dynamics across diverse scientific and engineering domains, we propose a novel and intuitive approach to continuous sequence modeling. Our method interprets time-series data as textitdiscrete samples from an underlying continuous dynamical system, and models its time evolution using Neural Stochastic Differential Equation (Neural SDE), where both the flow (drift) and diffusion terms are parameterized by neural networks. We derive a principled maximum likelihood objective and a textitsimulation-free scheme for efficient training of our Neural SDE model. We demonstrate the versatility of our approach through experiments on sequence modeling tasks across both embodied and generative AI. Notably, to the best of our knowledge, this is the first work to show that SDE-based continuous-time modeling also excels in such complex scenarios, and we hope that our work opens up new avenues for research of SDE models in high-dimensional and temporally intricate domains.