# Improving the Diversity of LLM Outputs without a Trade-off

arXiv: https://arxiv.org/abs/2609.33038 · HTML: https://mlsanity.com/paper/2609.33038/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 37 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Builds on (most cited first, 30 of 33)

- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [SmolLM2: When Smol Goes Big -- Data-Centric Training of a Small Language Model](https://mlsanity.com/paper/2502.02737/) (2025)
- [Stochastic Beams and Where to Find Them: The Gumbel-Top-k Trick for Sampling Sequences Without Replacement](https://mlsanity.com/paper/1903.06059/) (2019)
- [High Quality Rather than High Model Probability: Minimum Bayes Risk Decoding with Neural Metrics](https://mlsanity.com/paper/2111.09388/) (2021)
- [Language GANs Falling Short](https://mlsanity.com/paper/1811.02549/) (2018)
- [Jointly Reinforcing Diversity and Quality in Language Model Generations](https://mlsanity.com/paper/2509.02534/) (2025)
- [Comparison of Diverse Decoding Methods from Conditional Language Models](https://mlsanity.com/paper/1906.06362/) (2019)
- [No Prompt Left Behind: Exploiting Zero-Variance Prompts in LLM Reinforcement Learning via Entropy-Guided Advantage Shaping](https://mlsanity.com/paper/2509.21880/) (2025)
- [ProtoQA: A Question Answering Dataset for Prototypical Common-Sense Reasoning](https://mlsanity.com/paper/2005.00771/) (2020)
- [Diversity-Aware Policy Optimization for Large Language Model Reasoning](https://mlsanity.com/paper/2505.23433/) (2025)
- [Modifying Large Language Model Post-Training for Diverse Creative Writing](https://mlsanity.com/paper/2503.17126/) (2025)
- [Multilingual Prompting for Improving LLM Generation Diversity](https://mlsanity.com/paper/2505.15229/) (2025)
- [Incremental Sampling Without Replacement for Sequence Models](https://mlsanity.com/paper/2002.09067/) (2020)
- [Arithmetic Sampling: Parallel Diverse Decoding for Large Language Models](https://mlsanity.com/paper/2210.15458/) (2022)
- [Determinantal Beam Search](https://mlsanity.com/paper/2106.07400/) (2021)
- [On the Effect of Sampling Diversity in Scaling LLM Inference](https://mlsanity.com/paper/2502.11027/) (2025)
- [Representation-Based Exploration for Language Models: From Test-Time to Post-Training](https://mlsanity.com/paper/2510.11686/) (2025)
- [G2: Guided Generation for Enhanced Output Diversity in LLMs](https://mlsanity.com/paper/2511.00432/) (2025)
- [How Diversely Can Language Models Solve Problems? Exploring the Algorithmic Diversity of Model-Generated Code](https://mlsanity.com/paper/2503.00691/) (2025)
- [SetPO: Set-Level Policy Optimization for Diversity-Preserving LLM Reasoning](https://mlsanity.com/paper/2602.01062/) (2026)
- [Prune as You Generate: Online Rollout Pruning for Faster and Better RLVR](https://mlsanity.com/paper/2603.24840/) (2026)
- [Semantic-guided Diverse Decoding for Large Language Model](https://mlsanity.com/paper/2506.23601/) (2025)
- [Asking a Language Model for Diverse Responses](https://mlsanity.com/paper/2509.17570/) (2025)
- [Optimizing Diversity and Quality through Base-Aligned Model Collaboration](https://mlsanity.com/paper/2511.05650/) (2025)
- [3D-Prover: Diversity Driven Theorem Proving With Determinantal Point Processes](https://mlsanity.com/paper/2410.11133/) (2024)
- [Beyond Mode Collapse: Distribution Matching for Diverse Reasoning](https://mlsanity.com/paper/2605.19461/) (2026)
- [Free Lunch for Pass@k? Low Cost Diverse Sampling for Diffusion Language Models](https://mlsanity.com/paper/2603.04893/) (2026)
- [Quasi-random Multi-Sample Inference for Large Language Models](https://mlsanity.com/paper/2411.06251/) (2024)

## Abstract (arXiv)

We propose DAST (Diversifying Arithmetic Sampling with TokenTour), a method that increases the diversity of LLM outputs without any change to the marginal distribution and with negligible generation-time overhead (a few microseconds). We observe that token IDs are often arranged in a meaningless order and reassign them so that tokens with similar meanings appear consecutively. This can be done in advance in a few hundred seconds per model, and the resulting order can be reused for all subsequent generations. By combining this order with arithmetic sampling (or quasi-Monte Carlo methods), we make similar tokens less likely to be generated across runs while preserving the distribution. Our method not only produces qualitatively good ideas but also significantly improves performance on the downstream task of ProtoQA.