Harnessing Synthetic Data from Generative AI for Statistical Inference

Ahmad Abdel-Azim; Ruoyu Wang; Xihong Lin

stat.MLMar 5, 2026

Harnessing Synthetic Data from Generative AI for Statistical Inference

Authors: Ahmad Abdel-Azim, Ruoyu Wang, Xihong Lin

Organizations: Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA · Harvard University, Boston, Massachusetts 02115, USA

Abstract

The emergence of generative AI models has dramatically expanded the availability and use of synthetic data across scientific, industrial, and policy domains. While these developments open new possibilities for data analysis, they also raise fundamental statistical questions about when synthetic data can be used in a valid, reliable, and principled manner. This paper reviews the current landscape of synthetic data generation and use from a statistical perspective, with the goal of clarifying the assumptions under which synthetic data can meaningfully support downstream discovery, inference, and prediction. We survey major classes of modern generative models, their intended use cases, and the benefits they offer, while also highlighting their limitations and characteristic failure modes. We additionally examine common pitfalls that arise when synthetic data are treated as surrogates for real observations, including biases from model misspecification, attenuated uncertainty, and difficulties in generalization. Building on these insights, we discuss emerging frameworks for the principled use of synthetic data. We conclude with practical recommendations, open problems, and cautions intended to guide both method developers and applied researchers.

Figures & tables

Motivation	Target sampling distribution $Q$	Intended objective	Access pattern for $(\mathcal{O},\mathcal{S})$	Example methods
Privacy-preserving release	Single release: $Q=\widehat{P}_{\theta}\approx P$ ; Multiple releases: $Q(z)=\int\widehat{P}_{\theta}(z)\,p(\theta\mid\mathcal{O})\,d\theta$	Enable analysis without releasing individual-level records; propagate synthesis uncertainty or enforce a formal privacy guarantee.	Use $\mathcal{S}^{(1)},\dots,\mathcal{S}^{(M)}$ only (often multiple releases)	MI [ 95 , 91 , 30 ] ; DP-SGD [ 1 ] ; PATE [ 88 ] ; PrivBayes [ 138 ] ; PATE-GAN [ 52 ]
Data augmentation	Unconditional: $Q=\widehat{P}_{\theta}\approx P$ Conditional: $Q(\cdot)=\widehat{P}_{\theta}(\cdot\mid A=a)$ , or $\widehat{P}_{\theta}(\cdot\mid Y=1)$	Increase sample size and diversity for downstream learning (e.g., improved predictive performance, model tuning)	Use $\mathcal{O}\cup\mathcal{S}$ , with potential calibration or weighting steps	TabDDPM [ 61 ] ; SMOTE [ 20 ] ; CTAB-GAN [ 140 ] ; CTGAN [ 134 ] ; CoDSA [ 116 ]
Fairness	Constrained: $Q^{\star}\in\arg\min_{Q\in\mathcal{Q}}D(Q,\widehat{P}_{\theta})$ s.t. $\mathrm{Fair}(Q)\geq\tau$	Modify the training distribution to satisfy a fairness criterion while preserving utility.	Typically train/analyze on $\mathcal{O}\cup\mathcal{S}$ , or use $\mathcal{S}$ to reduce bias; protocols vary by fairness goal.	FairGAN [ 133 ] ; DECAF [ 120 ] ; TabFairGAN [ 93 ]
Domain transfer	Target-domain synthesis: $Q\approx P_{\lx@scalerel@obj{\mathcal{T}\mathstrut}}$ using training data $P\neq P_{\lx@scalerel@obj{\mathcal{T}\mathstrut}}$ ; covariate shift: $P_{\lx@scalerel@obj{\mathcal{T}\mathstrut}}(Y\mid X)=P(Y\mid X)$	Improve target performance under shift by evaluating on data matching the target environment.	Use synthetic transfer samples $\mathcal{S}\sim Q\approx P_{\lx@scalerel@obj{\mathcal{T}\mathstrut}}$ (with $\mathcal{O}\sim P$ ) to approximate training under $P_{\lx@scalerel@obj{\mathcal{T}\mathstrut}}$	IWCV [ 111 ] ; RadialGAN [ 136 ] ; Optimal transport [ 26 , 25 , 10 , 85 ]
Missing data/trajectory completion	Conditional completion: $Q=\widehat{P}_{\theta}(Z_{\text{miss}}\mid Z_{\text{obs}},A)$ ; Forecasting (special case): $Q=\widehat{P}_{\theta}(Z_{t_{0}+1:T}\mid Z_{1:t_{0}},A)$	Fill in missing data segments (e.g., forecast future) and/or generate plausible futures (e.g., digital twins).	Sample missing data (trajectories) conditioned on observed data (prefix); used for imputation, simulation, forecasting.	CSDI [ 113 ] ; TimeGAN [ 135 ] ; BRITS [ 16 ] ; DT-GPT [ 77 ]

Table 1: Different motivations for generating synthetic data

Model Class	Statistical Object(s)	Core Idea	Strengths and Limitations
Generative Adversarial Network (GAN)	Generator $G_{\theta_{1}}$ and discriminator $D_{\theta_{2}}$ (trained via adversarial loss)	Train a generator to produce samples indistinguishable from real data by a discriminator adversary.	Strengths: High sample fidelity, effective at matching data distribution support without explicitly modeling likelihood Limitations: Training can be unstable, susceptible to mode collapse where diversity of outputs is limited.
Variational Autoencoder (VAE)	Encoder $q_{\theta_{1}}(l\mid z)$ , decoder $p_{\theta_{2}}(z\mid l)$ ; ELBO objective $\mathbb{E}_{q_{\theta_{1}}(l\mid z)}[\log p_{\theta_{2}}(z\mid l)]-$ $\mathrm{KL}(q_{\theta_{1}}(l\mid z)\\|p(l))$	Encoder-decoder architecture; learn latent variable representation with tractable approximate inference via a lower bound (ELBO).	Strengths: Interpretable latent representations, principled probabilistic model, stable training Limitations: Sample quality often low-resolution due to surrogate loss, posterior collapse.
Normalizing Flows	Invertible transform $f_{\theta}$ ; exact likelihood with $\log p_{\theta}(z)$ via Jacobian determinant	Map a simple base distribution (e.g., Gaussian) through invertible functions to match data distribution	Strengths: Exact likelihood, smooth density modeling, invertible inference and sampling Limitations: Architecture can be constrained for tractability, challenging with discrete and high-dimensional data
Autoregressive / Transformer models	Factorized likelihood: $p_{\theta}(z)=\prod_{i}p_{\theta}(z_{i}\mid z_{<i})$ , attention weight matrices in transformer	Model joint distribution sequentially using conditional factors; transformers use self-attention to capture long-range dependencies.	Strengths: Tractable likelihood, excellent for conditional generation and prompt-based synthesis. Limitations: Sequential sampling is inherently slower, often requires huge data
Diffusion / Score-based models	Score function $s_{\theta}(z_{t},t)\approx\nabla_{z}\log p_{t}(z_{t})$ or reparameterization ( $\varepsilon_{\theta}$ , $z_{\theta}$ ); reverse SDE or denoising objective	Forward noising process followed by learned reverse denoising; data generated by iterative refinement	Strengths: State-of-the-art sample fidelity and diversity, stable training, natural conditional extensions Limitations: Expensive iterative refinement during sampling

Table 2: Comparison of deep generative model classes

Fig 1: An illustration of the difference between synthetic data-based and synthetic data-assisted approaches in the semisupervised regression context using AutoComplete [ 3 ] and SynSurr [ 79 ] as examples. AutoComplete pools the synthetic data and real data to conduct inference, while SynSurr uses synthetic data to construct $\hat{e}$ to assist the inference based on labeled data.

Fig 2: An illustration of RICE [ 130 ] – a regularization-based synthetic data-augmented method. To build a model to robustly classify images of diverse styles, RICE generates synthetic images of different styles (e.g., cartoon and photo) based on each real image (e.g., painting). The RICE training procedure impose regularization terms to encourage the model to perform similarly on real images and their synthetic counterparts.

Paradigm	Role of Synthetic Data	Target Distribution	Convergence Rate	Main Strengths and Limitations
Synthetic data–based	Treated as real data	$P_{\lx@scalerel@obj{\mathcal{T}\mathstrut}}=P$	Potentially improved if the model is correct	Strengths: simple and scalable Limitations: highly sensitive to generative model error and ignores synthesis uncertainty
Synthetic data–assisted	Auxiliary to real data	$P_{\lx@scalerel@obj{\mathcal{T}\mathstrut}}=P$	Same as real data-based methods (asymptotic variance can be improved)	Strengths: robust to generative model misspecification; Limitations: efficiency gains are usually limited to a constant level, no rate improvement
Synthetic data–augmented	Generate unseen or rare samples	$P_{\lx@scalerel@obj{\mathcal{T}\mathstrut}}\neq P$	Unclear	Strengths: can improve generalization and robustness to unseen heterogeneous target data Limitation: relies on strong prior knowledge for realistic augmentation
Synthetic in-context-learning	Generate synthetic tasks	$P_{\lx@scalerel@obj{\mathcal{T}\mathstrut}}\neq P$	Unclear	Strengths: learns general prediction and inference strategies across tasks and can automatically adapt to different problems without training Limitations: adaptivity and transferability depend on task realism

Table 3: Comparison of different paradigms for using synthetic data in downstream tasks.

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Valid Inference with Synthetic Data via Task Exchangeability

Lezhi Tan, Tijana Zrnic

Department of Management Science & Engineering Stanford University · Department of Statistics Stanford University

Synthetic Data Evaluation

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There is a proliferation of work arguing for the use of synthetic data in scientific research. For example, social scientists are arguing for the use of LLM-generated "silicon samples" in pilot studies; AI evaluations increasingly rely on "LLM-as-a-judge" outputs; and proteomics research is accelerated by generative models that produce synthetic protein structures. These developments raise an intriguing possibility: synthetic data may help researchers ask more questions, run more studies, and accelerate discovery. But they also raise a fundamental concern: synthetic data can be biased, noisy, and misspecified. In this work, we propose statistical principles for using synthetic data in scientific research with provable validity guarantees. The key insight is a new technical condition that we call task exchangeability. Informally, this is a requirement that the researcher can identify historical tasks, for which real data is available, such that their current task of interest is exchangeable with the historical tasks in an appropriate mathematical sense. We develop methods for valid inference under task exchangeability, together with extensions that provide guarantees even beyond exchangeability. We demonstrate the framework on public opinion surveys with silicon samples and AI evaluation with autoraters.

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