# Factorization-Error-Free Discrete Diffusion Language Model via Speculative Decoding

arXiv: https://arxiv.org/abs/2605.14305 · HTML: https://mlsanity.com/paper/2605.14305/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 26 of its 30 references that are in the map.
- First posted on arXiv 14 May 2026.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)
- Efficient LLM inference and serving / [Diffusion LLM and MoE inference](https://mlsanity.com/inference/diffusion-llm-and-moe-inference/)

## Builds on (most cited first, 26 of 26)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (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)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Dream 7B: Diffusion Large Language Models](https://mlsanity.com/paper/2508.15487/) (2025)
- [Lumiere: A Space-Time Diffusion Model for Video Generation](https://mlsanity.com/paper/2401.12945/) (2024)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [SeeSR: Towards Semantics-Aware Real-World Image Super-Resolution](https://mlsanity.com/paper/2311.16518/) (2023)
- [LLaDA2.0: Scaling Up Diffusion Language Models to 100B](https://mlsanity.com/paper/2512.15745/) (2025)
- [Discrete Copula Diffusion](https://mlsanity.com/paper/2410.01949/) (2024)
- [Self Speculative Decoding for Diffusion Large Language Models](https://mlsanity.com/paper/2510.04147/) (2025)
- [Error Bounds and Optimal Schedules for Masked Diffusions with Factorized Approximations](https://mlsanity.com/paper/2510.25544/) (2025)
- [Self-Speculative Masked Diffusions](https://mlsanity.com/paper/2510.03929/) (2025)
- [DEER: Draft with Diffusion, Verify with Autoregressive Models](https://mlsanity.com/paper/2512.15176/) (2025)

## Abstract (arXiv)

Discrete diffusion language models improve generation efficiency through parallel token prediction, but standard X0 prediction methods introduce factorization errors by approximating the clean token posterior with independent token-wise distributions. This paper proposes Factorization-Error-Free Discrete Diffusion Language Modeling (FeF-DLLM), which replaces independent clean-token prediction with an exact prefix-conditioned factorization of the clean posterior to better preserve token dependencies. To reduce the sequential cost introduced by prefix conditioning, FeF-DLLM further incorporates speculative decoding within diffusion denoising, accelerating inference while maintaining the parallel prediction and re-masking properties of DLLMs. Theoretically, we prove that FeF-DLLM generates from the true joint distribution and derive its expected acceleration ratio. Experiments on GSM8K, MATH, HumanEval, and MBPP demonstrate that our method improves accuracy by an average of 5.04 percentage points while achieving an average inference speedup of 3.86×.