Why Knowledge Distillation Works in Generative Models: A Minimal Working Explanation

TL;DR

This paper explains how knowledge distillation improves generative models by inducing a precision-recall trade-off, focusing on high-quality samples at the expense of diversity, validated through simulations and large language models.

Contribution

It offers a minimal, general explanation of KD's effectiveness in generative models, highlighting the precision-recall trade-off mechanism.

Findings

Distillation induces a trade-off between precision and recall in generative models.

Higher teacher selectivity leads to more focused, high-quality samples.

The precision-recall dynamics are validated in large-scale language models.

Abstract

Knowledge distillation (KD) is a core component in the training and deployment of modern generative models, particularly large language models (LLMs). While its empirical benefits are well documented -- enabling smaller student models to emulate the performance of much larger teachers -- the underlying mechanisms by which KD improves generative quality remain poorly understood. In this work, we present a minimal working explanation of KD in generative modeling. Using a controlled simulation with mixtures of Gaussians, we demonstrate that distillation induces a trade-off between precision and recall in the student model. As the teacher distribution becomes more selective, the student concentrates more probability mass on high-likelihood regions at the expense of coverage, which is a behavior modulated by a single entropy-controlling parameter. We then validate this effect in a large-scale language modeling setup using the SmolLM2 family of models. Empirical results reveal the same precision-recall dynamics observed in simulation, where precision corresponds to sample quality and recall to distributional coverage. This precision-recall trade-off in LLMs is found to be especially beneficial in scenarios where sample quality is more important than diversity, such as instruction tuning or downstream generation. Our analysis provides a simple and general explanation for the effectiveness of KD in generative modeling.