# Leveraging Pretrained Language Models as Energy Functions for Glauber Dynamics Text Diffusion

arXiv: https://arxiv.org/abs/2605.04291 · HTML: https://mlsanity.com/paper/2605.04291/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 28 of its 49 references that are in the map.
- First posted on arXiv 5 May 2026.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontiers](https://mlsanity.com/paper/2102.01454/) (2021)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Scaling Diffusion Language Models via Adaptation from Autoregressive Models](https://mlsanity.com/paper/2410.17891/) (2024)
- [Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusions](https://mlsanity.com/paper/2502.06768/) (2025)
- [Masked Diffusion Models are Secretly Time-Agnostic Masked Models and Exploit Inaccurate Categorical Sampling](https://mlsanity.com/paper/2409.02908/) (2024)
- [SSD-LM: Semi-autoregressive Simplex-based Diffusion Language Model for Text Generation and Modular Control](https://mlsanity.com/paper/2210.17432/) (2022)
- [The pitfalls of next-token prediction](https://mlsanity.com/paper/2403.06963/) (2024)
- [Likelihood-Based Diffusion Language Models](https://mlsanity.com/paper/2305.18619/) (2023)
- [Generator Matching: Generative modeling with arbitrary Markov processes](https://mlsanity.com/paper/2410.20587/) (2024)
- [KL Convergence Guarantees for Score diffusion models under minimal data assumptions](https://mlsanity.com/paper/2308.12240/) (2023)
- [PLANNER: Generating Diversified Paragraph via Latent Language Diffusion Model](https://mlsanity.com/paper/2306.02531/) (2023)
- [Limitations of Autoregressive Models and Their Alternatives](https://mlsanity.com/paper/2010.11939/) (2020)
- [Causal Language Modeling Can Elicit Search and Reasoning Capabilities on Logic Puzzles](https://mlsanity.com/paper/2409.10502/) (2024)
- [TESS 2: A Large-Scale Generalist Diffusion Language Model](https://mlsanity.com/paper/2502.13917/) (2025)
- [EdiTTS: Score-based Editing for Controllable Text-to-Speech](https://mlsanity.com/paper/2110.02584/) (2021)
- [Encoder-Decoder Gemma: Improving the Quality-Efficiency Trade-Off via Adaptation](https://mlsanity.com/paper/2504.06225/) (2025)
- [Evaluating Differentially Private Synthetic Data Generation in High-Stakes Domains](https://mlsanity.com/paper/2410.08327/) (2024)
- [Glauber Generative Model: Discrete Diffusion Models via Binary Classification](https://mlsanity.com/paper/2405.17035/) (2024)
- [Parallelising Glauber dynamics](https://mlsanity.com/paper/2307.07131/) (2023)

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

- [Discrete Diffusion Models via Evolving Variational Autoregressive Networks](https://mlsanity.com/paper/2609.27306/) (2026)

## Abstract (arXiv)

We present a discrete diffusion-based language model using Glauber dynamics from statistical physics. Our main insight is that instead of trying to train a discrete state space diffusion model using Glauber dynamics with a uniform transition kernel as the forward process, one can set up an ``energy function'' based on pretrained causal/masked language models. When viewed as the stationary distribution, this energy function allows us to significantly improve the quality of the generated text. Incorporating UL2 as the pretrained model into our diffusion pipeline, we outperform prior diffusion based LMs and perform competitively with autoregressive models of comparable model sizes. Furthermore, our models are competitive with or outperform prior diffusion models and GPT-2 style auto-regressive models on zero-shot common sense reasoning tasks as well as planning and search tasks like Sudoku and Zebra puzzles.