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Self-Consuming Generative Models Go MAD
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Analyzes self-consuming (autophagous) generative model loops across three data-mixing regimes and shows that without enough fresh real data, models progressively lose quality or diversity ("Model Autophagy Disorder").
Problem
Training successive generations of generative models on synthetic data from earlier generations creates an autophagous loop whose effects on quality (precision) and diversity (recall) are poorly understood.
Approach
Formalizes three autophagous loop families (fully synthetic, synthetic augmentation with fixed real data, fresh data) and a universal sampling-bias parameter lambda, then shows analytically (Gaussian martingale/supermartingale argument) and empirically (DDPM, StyleGAN2, WGAN-GP, GMM, normalizing flows) that without enough fresh real data the loop drifts MAD.
Key results
- Without sampling bias (lambda=1), fully synthetic loops show FID rising and both precision and recall decreasing over generations across DDPM, StyleGAN2, and WGAN-GP.
- With sampling bias, precision can stay stable or rise while recall drops faster, so FID still increases (e.g., lambda=0.8 MNIST DDPM, lambda=0.7 FFHQ StyleGAN2).
- In the fresh data loop, the limiting Wasserstein distance depends only on (n_r, n_s, lambda) and not on the initial model's sample size, and too much synthetic data beyond a threshold hurts the effective sample size.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train successive generations using only synthetic data, without sampling bias | Fully synthetic loop · MNIST and FFHQ | precision | Hurt |
| Train successive generations using only synthetic data, without sampling bias | Fully synthetic loop · MNIST and FFHQ | recall | Hurt |
| Add sampling bias (lower λ) during synthetic sampling | Fully synthetic loop · MNIST and FFHQ | precision | Helped |
| Add sampling bias (lower λ) during synthetic sampling | Fully synthetic loop · MNIST and FFHQ | recall | Hurt |
| Add sampling bias (lower λ) during synthetic sampling | Fully synthetic loop · MNIST and FFHQ | FID | Hurt |
| Keep a fixed real training dataset in each generation alongside synthetic data | Synthetic augmentation loop · MNIST and FFHQ | FID | Hurt |
| Keep a fixed real training dataset in each generation alongside synthetic data | Synthetic augmentation loop · MNIST and FFHQ | precision | Hurt |
| Keep a fixed real training dataset in each generation alongside synthetic data | Synthetic augmentation loop · MNIST and FFHQ | recall | Hurt |
| Add fresh real data at every generation | Fresh data loop · Gaussian modeling and MNIST DDPM | Wasserstein distance/FID | No clear effect |
| Add a modest amount of synthetic data alongside fresh real data | Fresh data loop · Gaussian modeling | effective sample size | Helped |
| Add synthetic data above the admissible threshold alongside fresh real data | Fresh data loop · Gaussian modeling | effective sample size | Hurt |
| Increase the amount of sampling bias (decrease λ) | Fresh data loop · Gaussian modeling | admissible synthetic sample threshold | Hurt |
Surprising findings
- Initial model influence is forgotten in the fresh data loop: the limiting distance is independent of n_ini.
- More sampling bias (smaller lambda) reduces the amount of synthetic data that can be used without harming performance in the Gaussian fresh data loop.
Limitations
- Experiments use small-scale image datasets (MNIST, 128x128 FFHQ) and simple generators rather than large-scale foundation models.
- Theory is proven only for Gaussian models; generalization to deep generative models is empirical.
- The paper does not provide a practical remedy beyond recommending fresh real data and synthetic-data detection or watermarking.
Experimental setup
Datasets: MNIST FFHQ 2D Rosenbrock distribution 25-mode GMM
Benchmarks: MNIST FFHQ
Metrics: FID precision recall Wasserstein distance effective sample size ratio
Baselines: fully synthetic loop synthetic augmentation loop
Builds on: DDPM StyleGAN2 WGAN-GP classifier-free guidance precision-recall metrics
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