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 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 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.