# A Tale of Two Temperatures: Simple, Efficient, and Diverse Sampling from Diffusion Language Models

arXiv: https://arxiv.org/abs/2604.09921 · HTML: https://mlsanity.com/paper/2604.09921/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 52 of its 56 references that are in the map.
- First posted on arXiv 10 Apr 2026.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 30 of 52)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [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)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Dream 7B: Diffusion Large Language Models](https://mlsanity.com/paper/2508.15487/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Fast-dLLM: Training-free Acceleration of Diffusion LLM by Enabling KV Cache and Parallel Decoding](https://mlsanity.com/paper/2505.22618/) (2025)
- [Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Models](https://mlsanity.com/paper/2503.09573/) (2025)
- [Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data](https://mlsanity.com/paper/2406.03736/) (2024)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [MMaDA: Multimodal Large Diffusion Language Models](https://mlsanity.com/paper/2505.15809/) (2025)
- [Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusions](https://mlsanity.com/paper/2502.06768/) (2025)
- [Autoregressive Diffusion Models](https://mlsanity.com/paper/2110.02037/) (2021)
- [Masked Diffusion Models are Secretly Time-Agnostic Masked Models and Exploit Inaccurate Categorical Sampling](https://mlsanity.com/paper/2409.02908/) (2024)
- [Scaling up Masked Diffusion Models on Text](https://mlsanity.com/paper/2410.18514/) (2024)
- [Is Self-Repair a Silver Bullet for Code Generation?](https://mlsanity.com/paper/2306.09896/) (2023)
- [d1: Scaling Reasoning in Diffusion Large Language Models via Reinforcement Learning](https://mlsanity.com/paper/2504.12216/) (2025)

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

- [Re-evaluating Confidence Remasking in Masked Diffusion Language Models](https://mlsanity.com/paper/2606.12232/) (2026)
- [From Interface to Inference: Eliciting Any-Order Inference from Any-Order Models](https://mlsanity.com/paper/2607.26504/) (2026)
- [Low-Confidence Remasking Traps Flexibility: Realizing Arbitrary-Order Potential for Diverse Rollouts in Diffusion LLMs](https://mlsanity.com/paper/2609.34509/) (2026)
- [Self-Repulsive Sampling for Diffusion Language Models](https://mlsanity.com/paper/2609.39560/) (2026)
- [Fork-dLLM: Avoiding the Flexibility Trap in Diffusion Language Models](https://mlsanity.com/paper/2609.39859/) (2026)

## Abstract (arXiv)

Much work has been done on designing fast and accurate sampling for diffusion language models (dLLMs). However, these efforts have largely focused on the tradeoff between speed and quality of individual samples; how to additionally ensure diversity across samples remains less well understood. In this work, we show that diversity can be increased by using softened, tempered versions of familiar confidence-based remasking heuristics, retaining their computational benefits and offering simple implementations. We motivate this approach by introducing an idealized formal model of fork tokens and studying the impact of remasking on the expected entropy at the forks. Empirically, the proposed tempered heuristics close the exploration gap (pass@k) between existing confidence-based and autoregressive sampling, hence outperforming both when controlling for cost (pass@NFE). We further study how the increase in diversity translates to downstream post-training and test-time compute scaling. Overall, our findings demonstrate that simple, efficient, and diverse sampling from dLLMs is possible.