# Diversity-Aware Reverse Kullback-Leibler Divergence for Large Language Model Distillation

arXiv: https://arxiv.org/abs/2604.00223 · HTML: https://mlsanity.com/paper/2604.00223/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 19 of its 26 references that are in the map.
- First posted on arXiv 31 Mar 2026.

## Placed in

- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 19 of 19)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [A Diversity-Promoting Objective Function for Neural Conversation Models](https://mlsanity.com/paper/1510.03055/) (2015)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Super-NaturalInstructions: Generalization via Declarative Instructions on 1600+ NLP Tasks](https://mlsanity.com/paper/2204.07705/) (2022)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [Improved Knowledge Distillation via Teacher Assistant](https://mlsanity.com/paper/1902.03393/) (2019)
- [Texygen: A Benchmarking Platform for Text Generation Models](https://mlsanity.com/paper/1802.01886/) (2018)
- [Unnatural Instructions: Tuning Language Models with (Almost) No Human Labor](https://mlsanity.com/paper/2212.09689/) (2022)
- [Decoupled Knowledge Distillation](https://mlsanity.com/paper/2203.08679/) (2022)
- [On the Efficacy of Knowledge Distillation](https://mlsanity.com/paper/1910.01348/) (2019)
- [Logit Standardization in Knowledge Distillation](https://mlsanity.com/paper/2403.01427/) (2024)
- [Decoupled Kullback-Leibler Divergence Loss](https://mlsanity.com/paper/2305.13948/) (2023)
- [Greedification Operators for Policy Optimization: Investigating Forward and Reverse KL Divergences](https://mlsanity.com/paper/2107.08285/) (2021)
- [MiniPLM: Knowledge Distillation for Pre-Training Language Models](https://mlsanity.com/paper/2410.17215/) (2024)
- [PromptKD: Distilling Student-Friendly Knowledge for Generative Language Models via Prompt Tuning](https://mlsanity.com/paper/2402.12842/) (2024)
- [Token-Scaled Logit Distillation for Ternary Weight Generative Language Models](https://mlsanity.com/paper/2308.06744/) (2023)
- [Weight-Inherited Distillation for Task-Agnostic BERT Compression](https://mlsanity.com/paper/2305.09098/) (2023)

## Built on by (most cited first, 5 of 5)

- [SimCT: Recovering Lost Supervision for Cross-Tokenizer On-Policy Distillation](https://mlsanity.com/paper/2605.07711/) (2026)
- [SEAD: Competence-Aware On-Policy Distillation via Entropy-Guided Supervision](https://mlsanity.com/paper/2606.28562/) (2026)
- [Consistently Informative Soft-Label Temperature for Knowledge Distillation](https://mlsanity.com/paper/2605.20357/) (2026)
- [Rethinking the Role of Temperature in Large Language Model Distillation](https://mlsanity.com/paper/2606.00306/) (2026)
- [SMOPD: Selective Token-Entropy Masking for Dirty-History Multi-Turn On-Policy Self-Distillation](https://mlsanity.com/paper/2608.14647/) (2026)

## Abstract (arXiv)

Reverse Kullback-Leibler (RKL) divergence has recently emerged as the preferred objective for large language model (LLM) distillation, consistently outperforming forward KL (FKL), particularly in regimes with large vocabularies and significant teacher-student capacity mismatch, where RKL focuses learning on dominant modes rather than enforcing dense alignment. However, RKL introduces a structural limitation that drives the student toward overconfident predictions. We first provide an analysis of RKL by decomposing its gradients into target and non-target components, and show that non-target gradients consistently push the target logit upward even when the student already matches the teacher, thereby reducing output diversity. In addition, RKL provides weak supervision over non-target classes, leading to poor tail alignment. To address these issues, we propose Diversity-aware RKL (DRKL), which removes this gradient effect and strengthens non-target supervision while preserving the optimization benefits of RKL. Extensive experiments across datasets and model families demonstrate that DRKL consistently outperforms FKL, RKL, and other state-of-the-art distillation objectives, achieving better performance and a superior fidelity-diversity trade-off.