The increasing need for data privacy and the demand for robust machine learning models have fueled the development of synthetic data generation techniques. However, current methods often succeed in replicating simple summary statistics but fail to preserve both the pairwise and higher-order correlation structure of the data that define the complex, multi-variable interactions inherent in real-world systems. This limitation can lead to synthetic data that is superficially realistic but fails when used for sophisticated modeling tasks. In this white paper, we introduce Generative Correlation Manifolds (GCM), a computationally efficient method for generating synthetic data. The technique uses Cholesky decomposition of a target correlation matrix to produce datasets that, by mathematical proof, preserve the entire correlation structure -- from simple pairwise relationships to higher-order interactions -- of the source dataset. We argue that this method provides a new approach to synthetic data generation with potential applications in privacy-preserving data sharing, robust model training, and simulation.

Survival analysis is a cornerstone of clinical research by modeling time-to-event outcomes such as metastasis, disease relapse, or patient death. Unlike standard tabular data, survival data often come with incomplete event information due to dropout, or loss to follow-up. This poses unique challenges for synthetic data generation, where it is crucial for clinical research to faithfully reproduce both the event-time distribution and the censoring mechanism. In this paper, we propose SurvDiff, an end-to-end diffusion model specifically designed for generating synthetic data in survival analysis. SurvDiff is tailored to capture the data-generating mechanism by jointly generating mixed-type covariates, event times, and right-censoring, guided by a survival-tailored loss function. The loss encodes the time-to-event structure and directly optimizes for downstream survival tasks, which ensures that SurvDiff (i) reproduces realistic event-time distributions and (ii) preserves the censoring mechanism. Across multiple datasets, we show that \survdiff consistently outperforms state-of-the-art generative baselines in both distributional fidelity and downstream evaluation metrics across multiple medical datasets. To the best of our knowledge, SurvDiff is the first diffusion model explicitly designed for generating synthetic survival data.

Numerous developments in the recent literature show the promising potential of deep learning in obtaining numerical solutions to partial differential equations (PDEs) beyond the reach of current numerical solvers. However, data-driven neural operators all suffer from the same problem: the data needed to train a network depends on classical numerical solvers such as finite difference or finite element, among others. In this paper, we propose a new approach to generating synthetic functional training data that does not require solving a PDE numerically. The way we do this is simple: we draw a large number $N$ of independent and identically distributed `random functions' $u_j$ from the underlying solution space (e.g., $H_0^1(\Omega)$) in which we know the solution lies according to classical theory. We then plug each such random candidate solution into the equation and get a corresponding right-hand side function $f_j$ for the equation, and consider $(f_j, u_j)_{j=1}^N$ as supervised training data for learning the underlying inverse problem $f \rightarrow u$. This `backwards' approach to generating training data only requires derivative computations, in contrast to standard `forward' approaches, which require a numerical PDE solver, enabling us to generate a large number of such data points quickly and efficiently. While the idea is simple, we hope that this method will expand the potential for developing neural PDE solvers that do not depend on classical numerical solvers.

In settings requiring synthetic data generation based on a clinical cohort, e.g., due to data protection regulations, heterogeneity across individuals might be a nuisance that we need to control or faithfully preserve. The sources of such heterogeneity might be known, e.g., as indicated by sub-groups labels, or might be unknown and thus reflected only in properties of distributions, such as bimodality or skewness. We investigate how such heterogeneity can be preserved and controlled when obtaining synthetic data from variational autoencoders (VAEs), i.e., a generative deep learning technique that utilizes a low-dimensional latent representation. To faithfully reproduce unknown heterogeneity reflected in marginal distributions, we propose to combine VAEs with pre-transformations. For dealing with known heterogeneity due to sub-groups, we complement VAEs with models for group membership, specifically from propensity score regression. The evaluation is performed with a realistic simulation design that features sub-groups and challenging marginal distributions. The proposed approach faithfully recovers the latter, compared to synthetic data approaches that focus purely on marginal distributions. Propensity scores add complementary information, e.g., when visualized in the latent space, and enable sampling of synthetic data with or without sub-group specific characteristics. We also illustrate the proposed approach with real data from an international stroke trial that exhibits considerable distribution differences between study sites, in addition to bimodality. These results indicate that describing heterogeneity by statistical approaches, such as propensity score regression, might be more generally useful for complementing generative deep learning for obtaining synthetic data that faithfully reflects structure from clinical cohorts.

There's no denying that biggest resource in the 21st century is data -- Data is often referred as the 4th industrial generation; companies who have adopted this model of collecting data and using it to make informed decisions are the ones who are thriving. But collecting data and generating experiments is not elementary as it sounds -- most mid level companies do not have the infrastructure or the resources to store scalable data. In most scenario's when you have to test a machine learning / AI model with no scalable data we have to generate synthetic data using machine learning. In some used cases synthetic data is generated because the company wants to keep its data confidential. Synthetic Data Vault (SDV) is a synthetic data generation ecosystem that allows a user to easily create synthetic data by learning from single table, multi-table, text and time series datasets.

A synthetic dataset is a data object that is generated programmatically, and it may be valuable to creating a single dataset from multiple sources when direct collection is difficult or costly. Although it is a fundamental step for many data science tasks, an efficient and standard framework is absent. In this paper, we study a specific synthetic data generation task called downscaling, a procedure to infer high-resolution, harder-to-collect information (e.g., individual level records) from many low-resolution, easy-to-collect sources, and propose a multi-stage framework called SYNC (Synthetic Data Generation via Gaussian Copula). For given low-resolution datasets, the central idea of SYNC is to fit Gaussian copula models to each of the low-resolution datasets in order to correctly capture dependencies and marginal distributions, and then sample from the fitted models to obtain the desired high-resolution subsets. Predictive models are then used to merge sampled subsets into one, and finally, sampled datasets are scaled according to low-resolution marginal constraints. We make four key contributions in this work: 1) propose a novel framework for generating individual level data from aggregated data sources by combining state-of-the-art machine learning and statistical techniques, 2) perform simulation studies to validate SYNC's performance as a synthetic data generation algorithm, 3) demonstrate its value as a feature engineering tool, as well as an alternative to data collection in situations where gathering is difficult through two real-world datasets, 4) release an easy-to-use framework implementation for reproducibility and scalability at the production level that easily incorporates new data.