# Diffusion-MF: Approximate Structured Diffusion for Sequence Labelling

arXiv: https://arxiv.org/abs/2606.18856 · HTML: https://mlsanity.com/paper/2606.18856/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 39 references that are in the map.
- First posted on arXiv 17 Jun 2026.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (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)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [Neural Architectures for Named Entity Recognition](https://mlsanity.com/paper/1603.01360/) (2016)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioning](https://mlsanity.com/paper/2208.04202/) (2022)
- [Conditional Random Fields as Recurrent Neural Networks](https://mlsanity.com/paper/1502.03240/) (2015)
- [Score-based Continuous-time Discrete Diffusion Models](https://mlsanity.com/paper/2211.16750/) (2022)
- [Deep Unfolding: Model-Based Inspiration of Novel Deep Architectures](https://mlsanity.com/paper/1409.2574/) (2014)
- [Loopy Belief Propagation for Approximate Inference: An Empirical Study](https://mlsanity.com/paper/1301.6725/) (2013)
- [Efficient Second-Order TreeCRF for Neural Dependency Parsing](https://mlsanity.com/paper/2005.00975/) (2020)
- [AIN: Fast and Accurate Sequence Labeling with Approximate Inference Network](https://mlsanity.com/paper/2009.08229/) (2020)
- [Bregman Conditional Random Fields: Sequence Labeling with Parallelizable Inference Algorithms](https://mlsanity.com/paper/2506.00732/) (2025)

## Abstract (arXiv)

We introduce Diffusion-MF, a discrete diffu- sion sequence labeller that places a linear-chain conditional random field (LCRF) inside the denoising loop. Unlike prior diffusion labellers, it performs structured inference at every step; parallel Mean-Field makes this efficient. Across multilingual POS, CoNLL-2003 NER, and joint Chinese Segmentation and POS, Diffusion-MF achieves the best primary result across all experimental settings.