Censored Flow Matching for Synthetic Time-to-Event Generation

Survival analysis models time-to-event data, but in clinical settings training data are costly and scarce: events accrue over years of follow-up, cohorts are small, and privacy regulations restrict sharing across institutions. Tabular generative models promise augmentation and privacy-preserving cohort sharing, yet are themselves data-hungry -- on the small cohorts typical of survival analysis, a single generator rarely characterizes the population well enough for downstream models trained on its output to match real-data performance. FoGS (Filtered Mixture-of-Generators for Survival analysis) reframes synthetic-data construction as sample selection rather than generation. A candidate pool is drawn from four architecturally distinct tabular generators, and each sample is scored by an ensemble of seven survival models trained on real data, using proper scoring rules as a per-sample plausibility proxy. A two-level pipeline optimizes, in its outer loop, a selection policy -- generator quotas, scorer weights, a random complement, and stratified balancing on event time and censoring -- against held-out downstream performance, while an inner loop tunes the downstream model (XGBoost-Cox). On 16 public datasets under train-on-synthetic, test-on-real (C-index and IBS, $0$--$100$ scale), FoGS yields mean improvements of $+2.17$ in C-index and $+0.67$ in IBS, improving both metrics on 9 of 16 datasets and at least one on 13 (one-sided Wilcoxon $p=0.039$ and $p=0.035$). It matches or exceeds real-data training on most cohorts, with no significant change in nearest-neighbour privacy margin relative to unfiltered sampling. Sample filtering over a heterogeneous generator pool is thus a viable substitute for real-data training in privacy-restricted clinical settings.

Functional data, i.e., random functions observed over a continuous domain, are increasingly available in areas such as biomedical research, health informatics, and epidemiology. However, effective statistical analysis for functional data is often hindered by challenges such as privacy constraints, sparse and irregular sampling, infinite-dimensionality, and non-Gaussian structures. To address these challenges, we introduce a novel framework named Smooth Flow Matching (SFM), tailored for generative modeling of functional data that enables statistical analysis without exposing sensitive real data. Under a copula framework, SFM constructs a semiparametric smooth flow to generate infinite-dimensional functional data, free of Gaussianity and low-rank assumptions. It is computationally efficient, handles irregular observations, and guarantees the smoothness of the generated functions, offering a practical and flexible solution in scenarios where existing deep generative methods are not applicable. Through extensive simulation studies, we demonstrate the advantages of SFM in terms of both synthetic data quality and computational efficiency. We then apply SFM to generate clinical trajectory data from the MIMIC-IV patient electronic health records (EHR) longitudinal database. Our analysis showcases the ability of SFM to produce high-quality surrogate data for downstream tasks, highlighting its potential to boost the utility of EHR data for clinical applications.

Survival analysis aims to estimate a time-to-event distribution from data with censored observations. Many existing methods either impose structural assumptions on the hazard function or discretize the time axis, which may limit flexibility and introduce approximation errors. We propose the Survival Diffusion Probabilistic Model (SDPM), a generative approach to continuous-time survival analysis. SDPM models the conditional distribution of the survival outcome, represented by the pair of observed time and censoring indicator, $\mathbb{P}(T,δ\mid \mathbf{x})$, using a denoising diffusion model. Under the assumption of conditionally independent censoring, conditional samples generated by the model can be transformed into survival function estimates using the Kaplan-Meier estimator. This formulation avoids parametric assumptions on the event-time distribution and does not require a discretization of the output time space. The model operates in a transformed target space, using standardized log-times and a continuous Gaussian-mixture representation of the censoring indicator. We evaluate SDPM on ten real survival datasets and compare it with five strong baselines, including tree-based, boosting-based, and neural survival models. Results show that SDPM achieves competitive predictive performance across C-index, integrated time-dependent AUC, and integrated Brier score. A study on synthetic Cox-Weibull data demonstrates that SDPM can recover the shape of an underlying continuous survival distribution more accurately than a strong nonparametric baseline when sufficiently many samples are generated. An ablation study confirms the importance of the proposed target-space transformations, which improve event-rate calibration, reduce invalid generated times, and provide consistent gains in predictive discrimination. Codes implementing the proposed model are publicly available.