# Jointly Reinforcing Diversity and Quality in Language Model Generations

arXiv: https://arxiv.org/abs/2509.02534 · HTML: https://mlsanity.com/paper/2509.02534/

## Key facts

- Cited by 80 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 83 references that are in the map.
- First posted on arXiv 2 Sep 2025.

## Builds on (most cited first, 30 of 61)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [A Diversity-Promoting Objective Function for Neural Conversation Models](https://mlsanity.com/paper/1510.03055/) (2015)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [WildChat: 1M ChatGPT Interaction Logs in the Wild](https://mlsanity.com/paper/2405.01470/) (2024)
- [Neural Text Generation with Unlikelihood Training](https://mlsanity.com/paper/1908.04319/) (2019)
- [From Crowdsourced Data to High-Quality Benchmarks: Arena-Hard and BenchBuilder Pipeline](https://mlsanity.com/paper/2406.11939/) (2024)
- [Texygen: A Benchmarking Platform for Text Generation Models](https://mlsanity.com/paper/1802.01886/) (2018)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Scaling Synthetic Data Creation with 1,000,000,000 Personas](https://mlsanity.com/paper/2406.20094/) (2024)
- [Understanding the Effects of RLHF on LLM Generalisation and Diversity](https://mlsanity.com/paper/2310.06452/) (2023)
- [L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning](https://mlsanity.com/paper/2503.04697/) (2025)
- [Can LLMs Generate Novel Research Ideas? A Large-Scale Human Study with 100+ NLP Researchers](https://mlsanity.com/paper/2409.04109/) (2024)
- [Diverse Beam Search: Decoding Diverse Solutions from Neural Sequence Models](https://mlsanity.com/paper/1610.02424/) (2016)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [Does Writing with Language Models Reduce Content Diversity?](https://mlsanity.com/paper/2309.05196/) (2023)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [Self-Improvement in Language Models: The Sharpening Mechanism](https://mlsanity.com/paper/2412.01951/) (2024)

## Built on by (most cited first, 30 of 80)

- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [Outcome-based Exploration for LLM Reasoning](https://mlsanity.com/paper/2509.06941/) (2025)
- [Evolving Language Models without Labels: Majority Drives Selection, Novelty Promotes Variation](https://mlsanity.com/paper/2509.15194/) (2025)
- [KL-Regularized Reinforcement Learning is Designed to Mode Collapse](https://mlsanity.com/paper/2510.20817/) (2025)
- [Diversity-Incentivized Exploration for Versatile Reasoning](https://mlsanity.com/paper/2509.26209/) (2025)
- [Towards Execution-Grounded Automated AI Research](https://mlsanity.com/paper/2601.14525/) (2026)
- [Look Inward to Explore Outward: Learning Temperature Policy from LLM Internal States via Hierarchical RL](https://mlsanity.com/paper/2602.13035/) (2026)
- [Entropy After </Think> for reasoning model early exiting](https://mlsanity.com/paper/2509.26522/) (2025)
- [Beyond the Sampled Token: Preserving Candidate Support in RLVR](https://mlsanity.com/paper/2510.14807/) (2025)
- [Representation-Based Exploration for Language Models: From Test-Time to Post-Training](https://mlsanity.com/paper/2510.11686/) (2025)
- [RESTRAIN: From Spurious Votes to Signals -- Self-Driven RL with Self-Penalization](https://mlsanity.com/paper/2510.02172/) (2025)
- [Rewarding the Rare: Uniqueness-Aware RL for Creative Problem Solving in LLMs](https://mlsanity.com/paper/2601.08763/) (2026)
- [String Seed of Thought: Prompting LLMs for Distribution-Faithful and Diverse Generation](https://mlsanity.com/paper/2510.21150/) (2025)
- [Save the Good Prefix: Precise Error Penalization via Process-Supervised RL to Enhance LLM Reasoning](https://mlsanity.com/paper/2601.18984/) (2026)
- [SetPO: Set-Level Policy Optimization for Diversity-Preserving LLM Reasoning](https://mlsanity.com/paper/2602.01062/) (2026)
- [Where does output diversity collapse in post-training?](https://mlsanity.com/paper/2604.16027/) (2026)
- [Random Policy Valuation is Enough for LLM Reasoning with Verifiable Rewards](https://mlsanity.com/paper/2509.24981/) (2025)
- [Can LLMs Guide Their Own Exploration? Gradient-Guided Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2512.15687/) (2025)
- [On-Policy Self-Distillation with Sampled Demonstrations Reduces Output Diversity](https://mlsanity.com/paper/2606.26091/) (2026)
- [MindGPT-4ov: An Enhanced MLLM via a Multi-Stage Post-Training Paradigm](https://mlsanity.com/paper/2512.02895/) (2025)
- [DSDR: Dual-Scale Diversity Regularization for Exploration in LLM Reasoning](https://mlsanity.com/paper/2602.19895/) (2026)
- [Expanding LLM Agent Boundaries with Strategy-Guided Exploration](https://mlsanity.com/paper/2603.02045/) (2026)
- [Exploring Multi-Temperature Strategies for Token- and Rollout-Level Control in RLVR](https://mlsanity.com/paper/2510.08892/) (2025)
- [Optimizing Diversity and Quality through Base-Aligned Model Collaboration](https://mlsanity.com/paper/2511.05650/) (2025)
- [Polychromic Objectives for Reinforcement Learning](https://mlsanity.com/paper/2509.25424/) (2025)
- [LaDi-RL: Latent Diffusion Reasoning Prevents Entropy Collapse in Reinforcement Learning](https://mlsanity.com/paper/2602.01705/) (2026)
- [Likelihood-Based Reward Designs for General LLM Reasoning](https://mlsanity.com/paper/2602.03979/) (2026)
- [Unveiling Implicit Advantage Symmetry: Why GRPO Struggles with Exploration and Difficulty Adaptation](https://mlsanity.com/paper/2602.05548/) (2026)
- [DPWriter: Reinforcement Learning with Diverse Planning Branching for Creative Writing](https://mlsanity.com/paper/2601.09609/) (2026)
- [Alternating Reinforcement Learning with Contextual Rubric Rewards: Beyond the Scalarization Strategy](https://mlsanity.com/paper/2603.15646/) (2026)

## Abstract (arXiv)

Post-training of Large Language Models (LMs) often prioritizes accuracy and helpfulness at the expense of diversity. This creates a tension: while post-training improves response quality, it also sharpens output distributions and reduces the range of ideas, limiting the usefulness of LMs in creative and exploratory tasks such as brainstorming, storytelling, or problem solving. We address this challenge with Diversity-Aware Reinforcement Learning (DARLING), a framework that jointly optimizes for response quality and semantic diversity. At its core, DARLING introduces a learned partition function to measure diversity beyond surface-level lexical variations. This diversity signal is then combined with a quality reward during online reinforcement learning, encouraging models to generate outputs that are both high-quality and distinct. Experiments across multiple model families and sizes show that DARLING generalizes to two regimes: non-verifiable tasks (instruction following and creative writing) and verifiable tasks (competition math). On five benchmarks in the first setting, DARLING consistently outperforms quality-only RL baselines, producing outputs that are simultaneously of higher quality and novelty. In the second setting, DARLING achieves higher pass@1 (solution quality) and pass@k (solution variety). Most strikingly, explicitly optimizing for diversity catalyzes exploration in online RL, which manifests itself as higher-quality responses.