A Continuous Time Markov Chain Framework for Insertion Language Models

Dhruvesh Patel, Benjamin Rozonoyer, Soumitra Das, Tahira Naseem, Tim G. J. Rudner, Andrew McCallum
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:874-882, 2026.

Abstract

Insertion Language Models (ILMs) offer several advantages over left-to-right generation and mask-based generation. However, existing formulations of insertion-based generation have largely been ad-hoc. In this paper, we derive a diffusion-style denoising objective for ILMs from first principles by formulating the noising process as a continuous-time Markov chain on the space of variable-length sequences. We show that previous formulations of ILMs can be viewed as special cases of this denoising framework. Through empirical evaluation on a synthetic planning task, we show that the proposed approach retains the benefits of insertion-based generation over left-to-right generation and masked diffusion models. In language modeling, our diffusion-based approach is competitive with left-to-right generation and masked diffusion models, while offering additional flexibility in sampling compared to existing insertion language models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-patel26a, title = { A Continuous Time Markov Chain Framework for Insertion Language Models }, author = {Patel, Dhruvesh and Rozonoyer, Benjamin and Das, Soumitra and Naseem, Tahira and Rudner, Tim G. J. and McCallum, Andrew}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {874--882}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/patel26a/patel26a.pdf}, url = {https://proceedings.mlr.press/v300/patel26a.html}, abstract = { Insertion Language Models (ILMs) offer several advantages over left-to-right generation and mask-based generation. However, existing formulations of insertion-based generation have largely been ad-hoc. In this paper, we derive a diffusion-style denoising objective for ILMs from first principles by formulating the noising process as a continuous-time Markov chain on the space of variable-length sequences. We show that previous formulations of ILMs can be viewed as special cases of this denoising framework. Through empirical evaluation on a synthetic planning task, we show that the proposed approach retains the benefits of insertion-based generation over left-to-right generation and masked diffusion models. In language modeling, our diffusion-based approach is competitive with left-to-right generation and masked diffusion models, while offering additional flexibility in sampling compared to existing insertion language models. } }
Endnote
%0 Conference Paper %T A Continuous Time Markov Chain Framework for Insertion Language Models %A Dhruvesh Patel %A Benjamin Rozonoyer %A Soumitra Das %A Tahira Naseem %A Tim G. J. Rudner %A Andrew McCallum %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-patel26a %I PMLR %P 874--882 %U https://proceedings.mlr.press/v300/patel26a.html %V 300 %X Insertion Language Models (ILMs) offer several advantages over left-to-right generation and mask-based generation. However, existing formulations of insertion-based generation have largely been ad-hoc. In this paper, we derive a diffusion-style denoising objective for ILMs from first principles by formulating the noising process as a continuous-time Markov chain on the space of variable-length sequences. We show that previous formulations of ILMs can be viewed as special cases of this denoising framework. Through empirical evaluation on a synthetic planning task, we show that the proposed approach retains the benefits of insertion-based generation over left-to-right generation and masked diffusion models. In language modeling, our diffusion-based approach is competitive with left-to-right generation and masked diffusion models, while offering additional flexibility in sampling compared to existing insertion language models.
APA
Patel, D., Rozonoyer, B., Das, S., Naseem, T., Rudner, T.G.J. & McCallum, A.. (2026). A Continuous Time Markov Chain Framework for Insertion Language Models . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:874-882 Available from https://proceedings.mlr.press/v300/patel26a.html.

Related Material