# HyperNSDE: Personalized Neural SDEs for Joint Static-Longitudinal Clinical Data Generation

arXiv: https://arxiv.org/abs/2610.07383 · HTML: https://mlsanity.com/paper/2610.07383/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 70 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Builds on (most cited first, 8 of 8)

- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise](https://mlsanity.com/paper/1906.02355/) (2019)
- [Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Data](https://mlsanity.com/paper/2402.14989/) (2024)
- [Synthetic Health-related Longitudinal Data with Mixed-type Variables Generated using Diffusion Models](https://mlsanity.com/paper/2303.12281/) (2023)
- [pySigLib -- Fast Signature-Based Computations on CPU and GPU](https://mlsanity.com/paper/2509.10613/) (2025)
- [STEB: In Search of the Best Evaluation Approach for Synthetic Time Series](https://mlsanity.com/paper/2505.21160/) (2025)

## Abstract (arXiv)

Synthetic patient data generation is a promising solution to the dual challenge of data scarcity and privacy constraints in healthcare machine learning. Realistic synthesis of patient-level clinical data requires jointly modeling heterogeneous static covariates, irregularly sampled longitudinal trajectories, and informative observation times - three tightly coupled components in practice yet rarely addressed together. We propose HyperNSDE, a continuous-time generative model that conditions a latent Neural SDE on static patient representations through a hypernetwork, allowing baseline characteristics to shape trajectory evolution beyond the initial condition without requiring a trajectory encoder, while stochastic latent dynamics capture realistic variability in generated paths. Observation times are modeled jointly through a latent-state-dependent intensity process, and training on irregular stochastic paths is stabilized via a deterministic-stochastic path decomposition with a non-adversarial signature-kernel objective. Experiments on simulated and real clinical datasets show improved observation-time fidelity and competitive performance, while matched-grid analyses reveal that forecasting and correlation metrics are affected by observation-grid regularity and trajectory smoothness.