As synthetic data proliferates across the Internet, it is often reused to train successive generations of generative models. This creates a ``self-consuming loop" that can lead to training instability or \textit{model collapse}. Common strategies to address the issue -- such as accumulating historical training data or injecting fresh real data -- either increase computational cost or require expensive human annotation. In this paper, we empirically analyze the latent space dynamics of self-consuming diffusion models and observe that the low-dimensional structure of latent representations extracted from synthetic data degrade over generations. Based on this insight, we propose \textit{Latent Space Filtering} (LSF), a novel approach that mitigates model collapse by filtering out less realistic synthetic data from mixed datasets. Theoretically, we present a framework that connects latent space degradation to empirical observations. Experimentally, we show that LSF consistently outperforms existing baselines across multiple real-world datasets, effectively mitigating model collapse without increasing training cost or relying on human annotation.

Large language models (LLM) have become state of the art in many benchmarks and conversational LLM applications like ChatGPT are now widely used by the public. Those LLMs can be used to generate large amounts of content which is posted on the internet to various platforms. As LLMs are trained on datasets usually collected from the internet, this LLM-generated content might be used to train the next generation of LLMs. Therefore, a self-consuming training loop emerges in which new LLM generations are trained on the output from the previous generations. We empirically study this self-consuming training loop using a novel dataset to analytically and accurately measure quality and diversity of generated outputs. We find that this self-consuming training loop initially improves both quality and diversity. However, after a few generations the output inevitably degenerates in diversity. We find that the rate of degeneration depends on the proportion of real and generated data.