arXiv:2509.08972v1 Announce Type: new Abstract: The increasing reliance on generative AI models has accelerated the generation rate of synthetic data, with some projections suggesting that most available new data for training could be machine-generated by 2030. This shift to a mainly synthetic content presents a critical challenge: repeated training in synthetic data leads to a phenomenon known as model collapse, where model performance degrades over generations of training, eventually rendering the models ineffective. Although prior studies have explored the causes and detection of model collapse, existing mitigation strategies remain limited. In this paper, we identify model overconfidence in their self-generated data as a key driver of collapse. Building on this observation, we propose a confidence-aware loss function that downweights high-confidence predictions during training. We introduce a novel loss function we call Truncated Cross Entropy (TCE). We demonstrate that TCE significantly delays model collapse in recursive training. We provide a model-agnostic framework that links the loss function design to model collapse mitigation and validate our approach both theoretically and empirically, showing that it can extend the model's fidelity interval before collapse by more than 2.3x. Finally, we show that our method generalizes across modalities. These findings suggest that the design of loss functions provides a simple yet powerful tool for preserving the quality of generative models in the era of increasing synthetic data.