No Single Best Model for Diversity: Learning a Router for Sample Diversity
Organizations: New York University · Stanford University · Carnegie Mellon University
Abstract
When posed with prompts that permit a large number of valid answers, comprehensively generating them is the first step towards satisfying a wide range of users. In this paper, we study methods to elicit a comprehensive set of valid responses. To evaluate this, we introduce diversity coverage, a metric that measures the total quality scores assigned to each unique answer in the predicted answer set relative to the best possible answer set with the same number of answers. Using this metric, we evaluate 18 LLMs, finding no single model dominates at generating diverse responses to a wide range of open-ended prompts. Yet, per each prompt, there exists a model that outperforms all other models significantly at generating a diverse answer set. Motivated by this finding, we introduce a router that predicts the best model for each query. On NB-WildChat, our trained router outperforms the single best model baseline (26.3% vs 23.8%). We further show generalization to an out-of-domain dataset (NB-Curated) as well as different answer-generation prompting strategies. Our work lays foundation for studying generating comprehensive answers when we have access to a suite of models.
Figures & tables
| Dataset | # Q | Example | |
| Question | Possible Valid Answers (delimited with ‘/’) | ||
| Simple Questions ( Zhang et al., 2024 ) | Output a random country in North America. | United States/ Canada/ Mexico / … | |
| NB-Curated 1 1 1 The original released dataset has 100 questions. We filter out 4 questions that ask for multiple answers (violating our hypothesis) and 4 questions that do not have multiple correct answers. ( Zhang et al., 2025b ) | Tell me a funny joke. | Who is Adam and why he is optimizing my code? / “Pick a lane” “Who’s Elaine?” | |
| NB-WildChat ( Zhang et al., 2025b ) | k | Give me a very simple way to remember the formula for tangent. | Tangent = / Draw a unit circle … |
| Infinity-Chat ( Jiang et al., 2026 ) | k | Write a story about America. | ”… I’m just like my country—I’m young, scrappy, and hungry, and I’m not throwin’ away my shot!” said Hamilton./ America was born in the streets. |
| SQ | Curated | WildChat | |
| Top overall model | |||
| Top two overall models | |||
| Random model / query | |||
| Top model / query | 97.9% | 59.6% | 33.0% |
| Method | NB-WildChat | NB-Curated (OOD) | ||||||
| #Unq | Qual | Unq Qual | Cov. | #Unq | Qual | Unq Qual | Cov. | |
| Top overall | 42.6 | 3.0 | 2.9 | 23.8% | 35.4 | 6.0 | 5.7 | 38.6% |
| Frequency | 33.1 | 3.8 | 3.6 | 21.0% | 28.2 | 7.2 | 7.1 | 39.6% |
| Random model per query | 27.8 | 3.7 | 3.6 | 18.1% | 27.8 | 7.2 | 7.0 | 37.5% |
| Top model per query (oracle) | 38.8 | 4.5 | 4.4 | 33.0% | 30.3 | 7.6 | 7.4 | 59.6% |
| KNN (N=1) | 34.3 | 3.7 | 3.6 | 23.1% | 28.2 | 7.3 | 7.1 | 39.7% |
| Method | NB-WildChat | NB-Curated (OOD) | ||||||
| #Unq | Qual | Unq Qual | Cov. | #Unq | Qual | Unq Qual | Cov. | |
| Top 2 overall | 39.1 | 3.4 | 3.2 | 23.8% | 31.6 | 6.7 | 6.3 | 38.3% |
| Top 2 per query | 40.7 | 4.5 | 4.5 | 35.8% | 41.3 | 7.7 | 7.6 | 62.6% |
| Router | 38.4 | 3.8 | 3.6 | 26.7% ∗∗ | 32.3 | 7.1 | 6.8 | 42.2% ∗∗ |
| Method | Prompt Template | ||
| Gen 1 | Gen 2 | Gen All | |
| Top overall | 18.5% | 19.7% | 23.8% |
| Random | 9.9% | 13.2% | 18.1% |
| Frequency | 15.6% | 17.1% | 21.0% |
| Oracle (G-1) | 25.6% | 22.3% | 20.4% |
| Oracle (G-2) | 19.5% | 28.3% | 21.0% |
Appendix figures & tables34 assets
Supplementary material from the paper’s appendix.
Appendix
| Model | Cov. | Qual | #Unq | Avg #Ans/Gen | Avg Ans. Len |
| Closed Source | |||||
| claude-sonnet-4-6 | 20.83% | 5.0 | 24.2 | 7.2 | 220.4 |
| gemini-3.1-flash-lite-preview | 21.48% | 4.4 | 27.5 | 6.6 | 62.1 |
| gemini-3.1-pro-preview | 19.78% | 4.4 | 23.7 | 6.7 | 162.1 |
| gpt-4o-mini | 18.79% | 3.9 | 28.1 | 8.7 | 44.4 |
| gpt-5.4 | 21.06% | 4.7 | 27.0 | 7.4 | 262.2 |
| Model | Mean LL | %Best | %Dom. | Raw Performance (Acc) |
| gemma-3-1b-it | 2.553 | 2.14% | 2.05% | 38.66% |
| Qwen3-0.6B | 2.553 | 0.28% | 0.26% | 40.34% |
| OLMo-2-0425-1B-Instruct | 1.489 | 1.05% | 0.93% | 40.61% |
| Llama-3.2-1B-Instruct | 1.245 | 0.80% | 0.67% | 48.40% |
| Qwen3-1.7B | 2.089 | 1.67% | 1.58% | 55.44% |
| gemma-3-4b-it | 2.495 | 4.70% | 4.50% | 57.57% |
| Model | Mean LL | %Best | %Dom. | Raw Performance (Acc) |
| Llama-3.2-1B-Instruct | 9.752 | 0.15% | 0.15% | 16.38% |
| gemma-3-1b-it | 11.766 | 0.15% | 0.15% | 24.49% |
| Qwen3-0.6B | 8.773 | 0.15% | 0.08% | 32.83% |
| Llama-3.2-3B-Instruct | 7.343 | 0.23% | 0.23% | 37.76% |
| Llama-3.1-8B-Instruct | 7.059 | 0.08% | 0.08% | 47.76% |
| OLMo-2-0425-1B-Instruct | 8.811 | 0.08% | 0.08% | 50.80% |
| Evaluation Data | ||||
| Method | NB-WildChat | Infinity-Chat | ||
| Random | 18.13% | 18.24% | ||
| Top Overall | 23.83% | 23.13% | ||
| Oracle | 33.04% | 30.50% | ||
| Training Data | Size | |||
| Router | NB-WildChat | 500 | 25.28% | 22.58% |
| Method | NB-WildChat | NB-Curated (OOD) | ||||||||
| Acc | #U | Q | UQ | Cov. | Acc | #U | Q | UQ | Cov. | |
| Top Overall | 19.5% | 42.6 | 3.0 | 2.9 | 23.8% | 3.4% | 35.4 | 6.0 | 5.7 | 38.6% |
| Random M / Q | 5.9% | 27.8 | 3.7 | 3.6 | 18.1% | 5.6% | 27.8 | 7.2 | 7.0 | 37.5% |
| Frequency | 12.0% | 33.1 | 3.8 | 3.6 | 21.0% | 9.0% | 28.2 | 7.2 | 7.1 | 39.6% |
| Top M / Q (oracle) | 100% | 38.8 | 4.5 | 4.4 | 33.0% | 100% | 30.3 | 7.6 | 7.4 | 59.6% |
| NN | 16.5% | 34.3 | 3.7 | 3.6 | 23.1% | 5.6% | 28.2 | 7.3 | 7.1 | 39.7% |
| Method | Gen 1 | Gen 2 | Gen All | ||||||
| #Unq | Quality | Cov. | #Unq | Quality | Cov. | #Unq | Quality | Cov. | |
| Random | 13.7 | 4.9 | 9.9% | 18.3 | 4.5 | 13.2% | 27.8 | 3.7 | 18.1% |
| Frequency | 25.4 | 3.9 | 15.6% | 25.2 | 4.1 | 17.1% | 33.1 | 3.8 | 21.0% |
| Top Overall | 31.8 | 3.2 | 18.5% | 34.8 | 3.1 | 19.7% | 42.6 | 3.0 | 23.8% |
| Oracle (G-1) | 32.8 | 4.1 | 25.6% | 32.1 | 3.7 | 22.3% | 31.0 | 3.3 | 20.4% |
| Oracle (G-2) | 24.1 | 4.3 | 19.5% | 32.3 | 4.7 | 28.3% | 31.6 | 3.3 | 21.0% |
| Gen 1 | Gen 2 | Gen All | ||||
| Cov. | Len | Cov. | Len | Cov. | Len | |
| Random | ||||||
| Top model | ||||||
| Top 2 models | ||||||
| Top model per query | ||||||
| Ratio | #Unq | Qual | Unq Qual | Cov. |
| Oracle model pair | ||||
| 0:50 | 42.50 | 4.16 | 3.95 | 35.40% |
| 5:45 | 43.90 | 4.11 | 3.94 | 36.82% |
| 10:40 | 45.00 | 4.13 | 3.99 | 37.56% |
| 15:35 | 45.50 | 4.09 | 3.88 | 37.10% |
| 20:30 | 46.30 | 3.93 | 3.80 | 36.46% |
| Strategy | #Unq | Qual | Unq Qual | Cov. |
| Oracle ratio | 44.80 | 3.66 | 3.55 | 32.58% |
| Overall best (40:10) | 46.20 | 2.99 | 2.98 | 27.62% |
| Half/half | 43.60 | 3.26 | 3.12 | 26.98% |
| #Unq | Qual | Unq Qual | Cov. | |
| 1 | 42.50 | 4.16 | 3.95 | 35.40% |
| 2 | 45.30 | 4.00 | 3.87 | 36.08% |
| 3 | 44.00 | 4.04 | 3.86 | 35.72% |
| 4 | 44.20 | 4.13 | 3.79 | 35.96% |
| 5 | 43.80 | 4.13 | 3.79 | 35.74% |
| 6 | 44.30 | 3.93 | 3.58 | 35.04% |
| #Unq | Qual | Unq Qual | Cov. | |
| 1 | 47.20 | 2.85 | 2.88 | 27.10% |
| 2 | 43.60 | 3.26 | 3.12 | 26.98% |
| 3 | 41.80 | 3.21 | 3.06 | 24.90% |
| 4 | 41.90 | 3.31 | 3.07 | 25.40% |
| 5 | 40.60 | 3.47 | 3.27 | 25.42% |
| 6 | 40.70 | 3.53 | 3.34 | 26.60% |
| #Unq | Qual | Unq Qual | Cov. | |
| 1 | 35.93 | 3.24 | 3.23 | 20.86% |
| 2 | 37.72 | 3.22 | 3.19 | 21.85% |
| 3 | 38.63 | 3.23 | 3.17 | 22.38% |
| 4 | 39.03 | 3.21 | 3.13 | 22.60% |
| 5 | 39.11 | 3.22 | 3.13 | 22.89% |
| 6 | 38.89 | 3.29 | 3.18 | 23.36% |
| Strategy | #Unq | Qual | Unq Qual | Cov. |
| Oracle | 44.10 | 3.93 | 3.73 | 34.24% |
| Best overall ( ) | 40.00 | 3.65 | 3.54 | 27.26% |
| Random | 39.23 | 3.53 | 3.35 | 25.25% |
| Prompt | Model | Cov. % | |||||
| 1 | 10 | 20 | 50 | 100 | 1000 | ||
| prompt_vanilla | Llama 8B | ||||||
| prompt_verbalized_all | |||||||
| system_vanilla | |||||||
| system_verbalized_all | |||||||
| prompt_vanilla | GPT-4o | ||||||
| Prompt | Model | Cov. % | ||||||
| 1 | 5 | 10 | 20 | 50 | 100 | 200 | ||
| prompt_vanilla | Llama 8B | |||||||
| prompt_verbalized_all | ||||||||
| system_vanilla | ||||||||
| system_verbalized_all | ||||||||
| prompt_vanilla | GPT-4o | |||||||
Diverse Text Generation
Diverse text generation studies how to produce varied, useful language outputs without sacrificing coherence, accuracy, or task performance.
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