Towards Theoretical Understandings of Self-Consuming Generative Models

TL;DR

This paper develops a theoretical framework to analyze how self-consuming training loops in generative models affect their learned data distributions, revealing phase transitions and bounds on distribution divergence.

Contribution

It introduces a rigorous theoretical analysis of self-consuming generative models, deriving bounds on distribution divergence and identifying phase transitions in training dynamics.

Findings

Total variation distance can be controlled with sufficient real data.

A phase transition occurs where divergence initially increases then decreases.

Insights into error propagation in kernel density estimation.

Abstract

This paper tackles the emerging challenge of training generative models within a self-consuming loop, wherein successive generations of models are recursively trained on mixtures of real and synthetic data from previous generations. We construct a theoretical framework to rigorously evaluate how this training procedure impacts the data distributions learned by future models, including parametric and non-parametric models. Specifically, we derive bounds on the total variation (TV) distance between the synthetic data distributions produced by future models and the original real data distribution under various mixed training scenarios for diffusion models with a one-hidden-layer neural network score function. Our analysis demonstrates that this distance can be effectively controlled under the condition that mixed training dataset sizes or proportions of real data are large enough. Interestingly, we further unveil a phase transition induced by expanding synthetic data amounts, proving theoretically that while the TV distance exhibits an initial ascent, it declines beyond a threshold point. Finally, we present results for kernel density estimation, delivering nuanced insights such as the impact of mixed data training on error propagation.