Distributional LLM-as-a-Judge

LLMs have emerged as powerful evaluators in the LLM-as-a-Judge paradigm, offering significant efficiency and flexibility compared to human judgments. However, previous methods primarily rely on single-point evaluations, overlooking the inherent diversity and uncertainty in human evaluations. This approach leads to information loss and decreases the reliability of evaluations. To address this limitation, we propose a novel training framework that explicitly aligns the LLMgenerated judgment distribution with human evaluation distributions. Specifically, we propose a distributional alignment objective based on KL divergence, combined with an auxiliary cross-entropy regularization to stabilize the training process. Furthermore, due to limited human annotations, empirical human distributions are merely noisy estimates of the true underlying distribution. We therefore incorporate adversarial training to ensure a robust alignment with this true distribution, rather than overfitting to its imperfect approximation. Extensive experiments across various LLM backbones and evaluation tasks demonstrate that our framework significantly outperforms existing closed-source LLMs and conventional singlepoint alignment methods, with superior alignment quality, strong robustness, and competitive evaluation accuracy.