Continuous Diffusion Models Can Obey Formal Syntax

Jinwoo Kim, Taylor Berg-Kirkpatrick, Loris D’Antoni
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:57136-57151, 2026.

Abstract

Diffusion language models offer a promising alternative to autoregressive models due to their global, non-causal generation process, but their continuous latent dynamics make discrete constraints—e.g., the output should be a JSON file that matches a given schema—difficult to impose. We introduce a training-free guidance method for steering continuous diffusion language models to satisfy formal syntactic constraints expressed using regular expressions. Our approach constructs an analytic score estimating the probability that a latent state decodes to a valid string accepted by a given regular expression, and uses its gradient to guide sampling, without training auxiliary classifiers. The denoising process targets the base model conditioned on syntactic validity. We implement our method in Diffinity on top of the PLAID diffusion model and evaluate it on 180 regular-expression constraints over JSON and natural-language benchmarks. Diffinity achieves 68-96% constraint satisfaction while incurring only a small perplexity cost relative to unconstrained sampling, outperforming autoregressive constrained decoding in both constraint satisfaction and output quality. Diffinity is open-sourced at github.com/large-loris-models/Diffinity.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-kim26b, title = {Continuous Diffusion Models Can Obey Formal Syntax}, author = {Kim, Jinwoo and Berg-Kirkpatrick, Taylor and D'Antoni, Loris}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {57136--57151}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/kim26b/kim26b.pdf}, url = {https://proceedings.mlr.press/v306/kim26b.html}, abstract = {Diffusion language models offer a promising alternative to autoregressive models due to their global, non-causal generation process, but their continuous latent dynamics make discrete constraints—e.g., the output should be a JSON file that matches a given schema—difficult to impose. We introduce a training-free guidance method for steering continuous diffusion language models to satisfy formal syntactic constraints expressed using regular expressions. Our approach constructs an analytic score estimating the probability that a latent state decodes to a valid string accepted by a given regular expression, and uses its gradient to guide sampling, without training auxiliary classifiers. The denoising process targets the base model conditioned on syntactic validity. We implement our method in Diffinity on top of the PLAID diffusion model and evaluate it on 180 regular-expression constraints over JSON and natural-language benchmarks. Diffinity achieves 68-96% constraint satisfaction while incurring only a small perplexity cost relative to unconstrained sampling, outperforming autoregressive constrained decoding in both constraint satisfaction and output quality. Diffinity is open-sourced at github.com/large-loris-models/Diffinity.} }
Endnote
%0 Conference Paper %T Continuous Diffusion Models Can Obey Formal Syntax %A Jinwoo Kim %A Taylor Berg-Kirkpatrick %A Loris D’Antoni %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-kim26b %I PMLR %P 57136--57151 %U https://proceedings.mlr.press/v306/kim26b.html %V 306 %X Diffusion language models offer a promising alternative to autoregressive models due to their global, non-causal generation process, but their continuous latent dynamics make discrete constraints—e.g., the output should be a JSON file that matches a given schema—difficult to impose. We introduce a training-free guidance method for steering continuous diffusion language models to satisfy formal syntactic constraints expressed using regular expressions. Our approach constructs an analytic score estimating the probability that a latent state decodes to a valid string accepted by a given regular expression, and uses its gradient to guide sampling, without training auxiliary classifiers. The denoising process targets the base model conditioned on syntactic validity. We implement our method in Diffinity on top of the PLAID diffusion model and evaluate it on 180 regular-expression constraints over JSON and natural-language benchmarks. Diffinity achieves 68-96% constraint satisfaction while incurring only a small perplexity cost relative to unconstrained sampling, outperforming autoregressive constrained decoding in both constraint satisfaction and output quality. Diffinity is open-sourced at github.com/large-loris-models/Diffinity.
APA
Kim, J., Berg-Kirkpatrick, T. & D’Antoni, L.. (2026). Continuous Diffusion Models Can Obey Formal Syntax. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:57136-57151 Available from https://proceedings.mlr.press/v306/kim26b.html.

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