Collapse

As AI-generated content increasingly populates the web, generative AI models are at growing risk of being trained on their own outputs, a process known as AI autophagy. This feedback loop has been shown to induce model collapse, typically characterized by a loss of diversity in generated content. However, existing work offers a limited understanding of this phenomenon and relies on mitigation strategies that assume access to human-authored data. In this paper, we conduct extensive simulations across multiple datasets and LLMs to address key gaps in the study of model collapse. First, we introduce model-intrinsic measures based on next-token probability distributions, showing that model collapse corresponds to an increasing concentration of probability mass on a small set of tokens. Second, we demonstrate that model collapse is also associated with a loss of common sense, as measured by a decline in commonsense inference accuracy. Third, we identify perplexity (a measure of model "surprise") as a key driver of collapse: fine-tuning on the least "surprising" documents leads to more severe degeneration. Building on this insight, we propose a perplexity-based filtering strategy that prioritizes high-surprise documents during fine-tuning. Unlike existing approaches, our method does not require distinguishing between human-authored and AI-generated content. Across datasets and LLM families, this strategy consistently mitigates model collapse, achieving performance comparable to, and in some cases better than, human-data baselines, while substantially reducing the concentration of next-token probabilities. Overall, our results provide a unified, model-centric understanding of model collapse and suggest practical, scalable strategies for training generative AI systems in increasingly synthetic environments.

Diffusion models achieve remarkable generation quality, yet face a fundamental challenge known as memorization, where generated samples can replicate training samples exactly. We develop a theoretical framework to explain this phenomenon by showing that the empirical score function (the score function corresponding to the empirical distribution) is a weighted sum of the score functions of Gaussian distributions, in which the weights are sharp softmax functions. This structure causes individual training samples to dominate the score function, resulting in sampling collapse. In practice, approximating the empirical score function with a neural network can partially alleviate this issue and improve generalization. Our theoretical framework explains why: In training, the neural network learns a smoother approximation of the weighted sum, allowing the sampling process to be influenced by local manifolds rather than single points. Leveraging this insight, we propose two novel methods to further enhance generalization: (1) Noise Unconditioning enables each training sample to adaptively determine its score function weight to increase the effect of more training samples, thereby preventing single-point dominance and mitigating collapse. (2) Temperature Smoothing introduces an explicit parameter to control the smoothness. By increasing the temperature in the softmax weights, we naturally reduce the dominance of any single training sample and mitigate memorization. Experiments across multiple datasets validate our theoretical analysis and demonstrate the effectiveness of the proposed methods in improving generalization while maintaining high generation quality.