# No Free Lunch for Synthetic Images under Data Scarcity Conditions

arXiv: https://arxiv.org/abs/2606.07640 · HTML: https://mlsanity.com/paper/2606.07640/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Robustness, privacy and adversarial aspects, one of 14 directions in Diffusion models.
- Builds on 21 of its 53 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Placed in

- Diffusion models / [Robustness, privacy and adversarial aspects](https://mlsanity.com/diffusion/robustness-privacy-and-adversarial-aspects/)

## Builds on (most cited first, 21 of 21)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Machine Learning for Synthetic Data Generation: A Review](https://mlsanity.com/paper/2302.04062/) (2023)
- [Differentially Private Diffusion Models](https://mlsanity.com/paper/2210.09929/) (2022)
- [An Introduction to Deep Generative Modeling](https://mlsanity.com/paper/2103.05180/) (2021)
- [No Free Lunch Theorem for Security and Utility in Federated Learning](https://mlsanity.com/paper/2203.05816/) (2022)
- [Diagnosing and Fixing Manifold Overfitting in Deep Generative Models](https://mlsanity.com/paper/2204.07172/) (2022)
- [SynthEval: A Framework for Detailed Utility and Privacy Evaluation of Tabular Synthetic Data](https://mlsanity.com/paper/2404.15821/) (2024)
- [Preventing Oversmoothing in VAE via Generalized Variance Parameterization](https://mlsanity.com/paper/2102.08663/) (2021)
- [A Gray-box Attack against Latent Diffusion Model-based Image Editing by Posterior Collapse](https://mlsanity.com/paper/2408.10901/) (2024)
- [Synthetic Tabular Data Validation: A Divergence-Based Approach](https://mlsanity.com/paper/2405.07822/) (2024)
- [Benchmarking Synthetic Tabular Data: A Multi-Dimensional Evaluation Framework](https://mlsanity.com/paper/2504.01908/) (2025)
- [Differentially Private Variational Autoencoders with Term-wise Gradient Aggregation](https://mlsanity.com/paper/2006.11204/) (2020)

## Abstract (arXiv)

This study investigates the trade-offs between fidelity, privacy, and utility in synthetic data generation under conditions of data scarcity and privacy sensitivity. We propose an evaluation framework that jointly assesses these three dimensions and apply it to three widely used generative models, VAE, GAN, and DDPM. The evaluation spans three image datasets, MNIST, OCTMNIST, and OrganAMNIST, encompassing both general-purpose and medical imaging domains. Notable differences arise between the three models in their behaviour when differential privacy mechanisms are introduced during training. GAN and DDPM demonstrate greater robustness, maintaining higher fidelity and downstream utility across a range of noise levels, while VAE degrades more rapidly as privacy constraints increase. This study highlights the importance of a multidimensional evaluation of deep generative models, also noting that their behaviour significantly differs when privacy techniques are applied.