Synthetic data

Working Definition

Synthetic data is data generated by a purpose-built mathematical model or algorithm—rather than directly measured or observed in the empirical world—used in place of, or alongside, real records to solve a specific analytical or machine-learning task. The generating model can range from differential equations and agent-based simulations, through multiple-imputation models in official statistics, to deep generative networks and large language models. Whereas everyday usage equates the term with “data made up by AI,” technical practice distinguishes between fully synthetic data (where no released record corresponds to a real individual) and partially synthetic data (where only sensitive attributes are replaced), evaluating every dataset along two competing axes at once: how much analytical utility it preserves and how much private information about the original sample it leaks.

Genesis and Global Lineage

The concept grew out of two parallel traditions that merged only after 2015. The first is official statistics and census disclosure control: in a landmark 1993 issue of the Journal of Official Statistics, Donald B. Rubin proposed that instead of releasing stripped-down census microdata that could still be re-identified, statistical agencies should treat non-sampled citizens as missing data and release fully synthetic microdata generated via multiple imputation; in the same issue, Roderick J. A. Little formulated the partially synthetic variant. Developed further by Trivellore Raghunathan, Jerome Reiter, and Jörg Drechsler, this lineage gave rise to synthetic public-use census files and clinical registries, always motivated by disclosure limitation rather than data scarcity. The second source is machine learning and computer vision: data augmentation, 3D physics simulators for robotics and autonomous driving, and—after 2014—Generative Adversarial Networks (GANs), variational autoencoders, diffusion models, and LLMs, which made sampling realistic high-dimensional records routine. The 2022 Royal Society report by James Jordon, Łukasz Szpruch, and coauthors (Synthetic Data – what, why and how?), which serves as our canonical source, unifies both traditions under a single definition while issuing a sharp warning against commercial hype: vendor slogans selling synthetic data as instant “privacy by design” conflate the absence of real row identifiers with genuine mathematical privacy.

Central European Lineage

An important mathematical anticipation of this principle leads back to interwar Central Europe through Stanisław Ulam (and alongside him, Budapest-born John von Neumann). In defining synthetic data, the canonical Royal Society report by Jordon, Szpruch (himself a Polish mathematician working in Edinburgh and at the Alan Turing Institute), and coauthors explicitly traces the idea of computer-generated data “at least” back to Ulam and von Neumann’s invention of the Monte Carlo method in the late 1940s—the insight that a physical or statistical system too complex for closed-form calculation can be studied by drawing artificial random samples from a formal model on a computer. Ulam received his entire mathematical formation in interwar Lwów (then Poland, now Lviv, Ukraine): he studied at Lwów Polytechnic (Politechnika Lwowska), defended his doctorate there in 1933 under Kazimierz Kuratowski, and was a central figure in the Lwów School of Mathematics gathered around Stefan Banach and the Scottish Café (Kawiarnia Szkocka) before leaving Poland in August 1939. While the Monte Carlo method itself was formulated at Los Alamos (conceived in 1946 and published by Nicholas Metropolis and Ulam in 1949) to model neutron diffusion rather than to protect personal data, the canonical literature on synthetic data explicitly recognizes it as the conceptual ancestor of replacing costly empirical observation with controlled simulation.

Why Now

Three developments between 2018 and 2026 propelled synthetic data from a specialist statistical technique into the center of technology policy and AI engineering. First, data-protection regulation: the EU’s General Data Protection Regulation (GDPR, in force since May 2018) raised the legal cost of sharing personal data across hospital, banking, and telecom silos, creating a booming market for platforms promising synthetic datasets outside GDPR scope. That commercial wave triggered a decisive scientific pushback led by Theresa Stadler, Bristena Oprisanu, and Carmela Troncoso (Synthetic Data – Anonymisation Groundhog Day, USENIX Security 2022), who proved quantitatively that standard generative models either leak membership and attribute information about outlier records or destroy the statistical correlations analysts need. Second, the exhaustion of high-quality human text for frontier AI: as public web corpora reached saturation, AI labs turned heavily to training models on synthetic text, code, and reasoning traces generated by other models (distillation, self-play, synthetic instruction tuning)—a shift whose failure mode Ilia Shumailov and colleagues diagnosed in 2023–2024 as model collapse. Third, institutional adoption by the UK Office for National Statistics (ONS), the U.S. Census Bureau, and national health-data authorities brought the issue into administrative law, forcing regulators to decide when a synthetic registry can safely guide public policy.

Explanatory Power

The concept forces analysts to separate three questions that organizational practice routinely blurs: where a record came from, what valid inferences it supports, and whether an adversary can link it to a real person. First, it explains why “artificial” never automatically means “anonymous”: an overparameterized generative model fitted to a small clinical dataset can memorize rare patient profiles nearly verbatim, making the corporate assumption that synthetic data automatically escapes GDPR obligations an untested hypothesis. Second, it clarifies why systems trained on synthetic data perform well on typical cases while failing at the margins: a statistical generator reproduces the dense center of a distribution while smoothing away its heavy tails, where rare diseases, demographic minorities, and black-swan failures reside. Third, it exposes a feedback loop in the digital commons: model-generated text and images flood the open web, crawlers ingest them into the next training corpus, and subsequent models learn the stylistic priors of earlier generators rather than empirical reality.

Axes of Debate

Underappreciated Angle

Public and technical debates rarely confront the epistemic status of synthetic data as historical and scientific evidence. An empirical dataset—however noisy—is a causal trace of events in the world independent of the investigator’s theory; a synthetic dataset is the deductive output of a model dressed in the tabular or visual format of an observation. When synthetic records enter a clinical archive, economic benchmark, or administrative proceeding without indelible provenance metadata, the evidentiary chain silently flips: an artifact in the data is no longer a measurement error correctable by inspecting the instrument, but a theoretical assumption baked into the generator masquerading as empirical confirmation of itself. Just as a facsimile reconstructed from a model of a lost manuscript is not a primary source, the most important institutional norm for the synthetic era may be mandatory, machine-readable provenance tagging that prevents model projections from being mistaken for fresh observations of reality.