Smooth Flow Matching for Synthesizing Functional Data

Generating time-to-event data is increasingly important in survival analysis, but it remains statistically challenging because event times are often censored and thus prevent flexible generative modeling. To fill this gap, we propose a novel method called censored flow matching (CFM), aiming at providing a flexible flow-based generative mechanism for synthesizing time-to-event data as well as learning their corresponding probabilistic densities. Unlike existing methods, CFM does not rely on survival likelihoods to handle censoring, but instead exploits the monotonicity property of differential flows to address censoring via pullback sampling. Under this framework, we implement an alternating procedure between pullback sampling and CFM steps, leading to a flow-based expectation--maximization (EM) algorithm tailored for time-to-event inference. Under mild distributional conditions, we establish the convergence of CFM to the true event-time distribution as the EM iterations proceed. We then apply CFM to generate time-to-event data and estimate their probabilistic densities, where the observed censoring time can be incorporated to provide truncated sampling or truncated density estimation for survival inference. Through extensive simulation studies, we demonstrate the benefits of CFM for complex and large-scale data generation. Finally, we apply CFM to analyze data from the Organ Procurement and Transplantation Network (OPTN) and the Medical Information Mart for Intensive Care IV (MIMIC-IV), showcasing its benefits for synthetic and predictive survival analyses in terms of data fidelity, predictive performance, and empirical privacy characteristics.

Recent advances in generative modeling have substantially improved time series generation, yet most existing methods either assume a regular temporal grid or focus on feature dynamics under a given sampling structure. This makes them illsuited for generating irregular time series in their native form, where a model must capture not only feature values, but also how many observations occur, when they occur, and which features are observed together. To address this heterogeneous generation problem, we propose ChronoFlow, a unified hierarchical flow matching framework organized by statistical granularity. Following a coarse-to-fine hierarchy, ChronoFlow first generates observation counts and feature-wise frequencies, then jointly generates observation times and feature co-observation patterns, and finally generates values conditioned on the realized pattern. This turns a complex joint generation problem into structurally aligned subproblems while preserving their dependencies. To evaluate complete irregular time series generation, we introduce complementary metrics spanning sample realism, sampling structure, value fidelity, and temporal and cross-feature dependencies, and validate them through controlled corruptions. Across five benchmarks, ChronoFlow achieves strong improvements in generation fidelity over existing baselines, while factorization studies support the proposed hierarchy. Our code is available at https://anonymous.4open.science/r/ChronoFlow.

Synthetic medical tabular data generation has become essential for developing and validating computer-based medical systems (CBMSs) when real clinical data is restricted due to privacy, ethical, or data availability limitations. Existing probabilistic and deep generative models often lack interpretability and fail to preserve clinically meaningful dependencies, limiting their suitability for safety-critical applications. This paper proposes a novel application of Fuzzy Cognitive Maps (FCMs) in a framework for synthetic medical tabular data generation with explicit causality and privacy preservation. Clinical features are described using linguistically interpretable fuzzy sets, and inter-feature dependencies are encoded as FCM edge weights computed from fuzzy set intersections. Synthetic patient records are generated by propagating randomly initialized linguistic activation vectors through the FCM until convergence, followed by defuzzification to produce clinically coherent numerical values. The approach natively handles mixed data types, and domain constraints common in health records. Experimental evaluation on UCI medical benchmark datasets demonstrates competitive performance under a Train-on-Synthetic-Test-on-Real (TSTR) protocol. The proposed method achieves accuracy of up to 0.81 and AUROC of up to 0.90 on the Heart Disease dataset, matching or exceeding TVAE and Gaussian Copula baselines while running exclusively on CPU. Fidelity metrics including KS Complement (up to 0.91) and Correlation Similarity (up to 0.95) confirm strong statistical coherence, and DCR Baseline Protection scores consistently exceed those of TVAE, confirming adequate privacy guarantees. These results demonstrate that causally grounded, interpretable fuzzy modeling offers a computationally efficient and transparent alternative to deep generative models for trustworthy synthetic data generation in CBMSs.