# Dist2ill: Distributional Distillation for One-Pass Uncertainty Estimation in Large Language Models

arXiv: https://arxiv.org/abs/2505.11731 · HTML: https://mlsanity.com/paper/2505.11731/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 56 of its 83 references that are in the map.
- First posted on arXiv 16 May 2025.

## Builds on (most cited first, 30 of 56)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)

## Built on by (most cited first, 1 of 1)

- [CGES: Confidence-Guided Early Stopping for Efficient and Accurate Self-Consistency](https://mlsanity.com/paper/2511.02603/) (2025)

## Abstract (arXiv)

Large Language Models (LLMs) often exhibit misalignment between the quality of their generated responses and the confidence estimates they assign to them. Bayesian treatments, such as marginalizing over a reliable weight posterior or over the space of reasoning traces, provide an effective remedy, but incur substantial computational overhead due to repeated sampling at test time. To enable accurate uncertainty estimation in a single forward pass, we propose a novel distributional distillation framework (Dist2ill) that trains an LLM to produce multiple diverse reasoning paths within one inference pass, while using a lightweight parametric module to approximate empirical confidence scores derived from the sampling distribution. Extensive experiments demonstrate that Dist2ill preserves reasoning diversity and achieves state-of-the-art uncertainty estimation, substantially improving Expected Calibration Error (ECE) and Negative Log-Likelihood (NLL), while remaining computationally efficient.