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

Perrine Chassat; Agathe Guilloux

stat.MLOct 5, 2026

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

Authors: Perrine Chassat, Agathe Guilloux

Organizations: Inria, Université Paris Cité, Inserm, HeKA F-75015 Paris, France

Abstract

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.

Figures & tables

Model	Static	Irregular	Continuous	Joint modeling	Modeled
Model	data	time-series	latent	static/TS	intensity
TimeGAN Yoon et al. (2019)	×	×	×	×	×
EHR-M-GAN Li et al. (2023)	×	×	×	×	×
TimeDiff Tian et al. (2024)	× 3 3 footnotemark: 3	×	×	× 3 3 footnotemark: 3	×
EHR-Safe Yoon et al. (2023)	✓	✓	×	✓	×
LatentODE Rubanova et al. (2019)	×	✓	✓	×	✓

Table 1: Comparison of generative models for joint static and irregular longitudinal data.

{}^{\text{1}}

Irregular timing handled externally.

{}^{\text{2}}

Static covariates conditioned on, not generated.

{}^{\text{3}}

Static variables represented as time-series channels.

Figure 1: HyperNSDE generation pipeline. Generating a synthetic subject follows a hierarchical process (Appendix A.3 ). Static latent representations are sampled from the HI-VAE learned distributions, decoded into synthetic covariates, and passed through the hypernetwork to generate patient-specific SDE parameters. A latent path is then simulated from the personalized Neural SDE and decoded at observation times sampled from the intensity network to produce synthetic irregular longitudinal trajectories. Original longitudinal data are used only at training time via the loss terms, without relying on a longitudinal encoder. Solid arrows denote deterministic computations; dashed arrows denote stochastic steps.

Figure 2: Qualitative comparison of real and generated longitudinal trajectories. Rows denote datasets and columns the real data and generative methods. Trajectory color represents the static covariates: blue trajectories have $W_{1}=0$ and red ones have $W_{1}=1$ , with color intensity encoding the continuous covariate $W_{0}$ . For the simulated data, $W_{0}\in[-0.79,0.73]$ and the plotted variable is $x_{0}$ ; for VELOUR, $W_{0}$ is age ( $22$ – $79$ years), $W_{1}$ is sex, and the plotted variable is hemoglobin; for PPMI, $W_{0}$ is years of education ( $0$ – $30$ ), $W_{1}$ is sex, and the plotted variable is supine diastolic blood pressure. Additional simulated-data results are in Appendix F .

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 3: Pareto front between the longitudinal deterministic reconstruction loss

\mathcal{L}_{\mathrm{long,det}}

and the static reconstruction loss

\mathcal{L}_{\mathrm{static}}

. Each point corresponds to a non-dominated hyperparameter configuration found by Optuna for our model on the reference simulated-data setting.

Hyperparameter	Range / Values	Type
Batch size	$\{128,256\}$	categorical
Learning rate	$\{10^{-4},10^{-3},2\cdot 10^{-3},5\cdot 10^{-3},10^{-2}\}$	categorical
Static latent dims. $d_{\mathrm{s}}$ , $d_{\mathrm{u}}$	$[2,\,8]$	integer
Longitudinal latent dim. $d_{\mathrm{z}}$	$[2,\,d_{\mathrm{z}}]$	integer
Hidden dim.	$\{16,32,64,128\}$	categorical
ODE/SDE layers	$[1,\,4]$	integer

Appendix

Table 5: Hyperparameter search space.

Dataset	Patients	Long.	Static	Common	Avg. observed	Time span
Dataset	Patients	variables	variables	grid points	visits/patient	(days)
VELOUR	526	23	26	673	21.3	23–990
PPMI	1930	15	20	686	11.2	153–5448

Appendix

Table 6: Summary statistics of the real-world datasets after preprocessing.

Metric	vs MultiNODEs	vs RTSGAN	vs DGBFGP+HIVAE
MMD longi $\downarrow$	$-2378.8^{***}$ ✓	$-1.242^{***}$ ✓	$-103.6^{***}$ ✓
MMD static $\downarrow$	$-0.0026^{**}$ ✓	$-0.0048^{***}$ ✓	$-0.0026^{***}$ ✓
Corr. RMSE longi $\downarrow$	$+0.020$ n.s.	$+0.007$ n.s.	$-0.064$ n.s.
Corr. RMSE static $\downarrow$	$-0.004$ n.s.	$-0.027^{*}$ ✓	$-0.014$ n.s.
Discrim. Score $\downarrow$	$-0.035^{***}$ ✓	$-0.002$ n.s.	$-0.037^{***}$ ✓
KL $\lambda$ $\downarrow$	$-66.86^{***}$ ✓	$0.138^{*}$ ×	$-66.86^{***}$ ✓

Appendix

Table 9: Paired Wilcoxon signed-rank tests, HyperNSDE vs each baseline.

N_{\mathrm{MC}}=30

seeds (the 50 generations averaged within each seed before pairing), two-sided, Holm-corrected across all 30 tests. Cells show the median difference (HyperNSDE vs. baseline); the sign is oriented per metric so that ✓ marks where HyperNSDE is significantly better and × where significantly worse.

{}^{*}\,p<.05

{}^{**}\,p<.01

{}^{***}\,p<.001

; n.s. = not significant after correction.

Model	Static only	Pattern only	Values only	All (Table 2)
Reference	$0.493$	$0.511$	$0.480$	$0.499$
MultiNODEs	$0.486$	$1.000$	$0.998$	$0.998$
RTSGAN	$\mathbf{0.522}$	$1.000$	$0.947$	$0.932$
DGBFGP + HIVAE	$0.487$	$1.000$	$0.999$	$0.999$
HyperNSDE	$0.462$	$\mathbf{0.760}$	$\mathbf{0.942}$	$\mathbf{0.926}$

Appendix

Table 11: C2ST test AUROC by classifier input (simulated data). Values closer to 0.5 are better (harder to distinguish from real). Best non-reference value per column in bold .

Static covariate	SMD (median)	p-value (median [Q1, Q3])
SEX	$0.152$	$0.334$ $[0.213,0.582]$
RACE	$0.186$	$0.424$ $[0.184,0.595]$
REGION	$0.221$	$0.635$ $[0.462,0.889]$
Age category	$0.010$	$0.594$ $[0.343,0.812]$
ECOG Performance Status	$0.136$	$0.625$ $[0.352,0.790]$
Height	$0.013$	$0.560$ $[0.422,0.855]$

Appendix

Table 19: Real-vs-synthetic static-covariate fidelity on VELOUR for HyperNSDE . For each covariate, the standardized mean difference (SMD;

<0.1

indicates negligible differences) and the real-vs-synthetic test p-value are computed against the real cohort and summarised across the 50 generated cohorts (median [Q1, Q3]). High p-values indicate the synthetic covariate is statistically indistinguishable from the real one.

Figure 4: Qualitative comparison of HyperNSDE and baselines on simulated data. Rows correspond to the three longitudinal variables

x_{0}

x_{1}

x_{2}

; columns compare the original data against HyperNSDE and baselines.

y

-axis limits are shared across columns per row. The color encodes

W_{0}

separately for subjects with

W_{1}=0

(blue gradient) and

W_{1}=1

(red gradient).

Figure 5: Qualitative comparison of HyperNSDE generation modes on simulated data. Rows correspond to the three longitudinal variables

x_{0}

x_{1}

x_{2}

; columns compare the original data and its deterministic component against HyperNSDE under posterior sampling, prior sampling, and estimated deterministic component. The color encodes

W_{0}

separately for subjects with

W_{1}=0

(blue gradient) and

W_{1}=1

(red gradient).

Figure 6: Qualitative comparison of ablation study variants on simulated data. Rows correspond to the three longitudinal variables $x_{0}$ , $x_{1}$ , $x_{2}$ ; columns compare the original data and HyperNSDE against the ablation variants described in Appendix E.4 . The color encodes $W_{0}$ separately for subjects with $W_{1}=0$ (blue gradient) and $W_{1}=1$ (red gradient).

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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.

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