{"slug": "continuous-diffusion-models-can-obey-formal-syntax", "title": "Continuous Diffusion Models Can Obey Formal Syntax", "summary": "Researchers introduced Diffinity, a training-free guidance method that enables continuous diffusion language models to satisfy formal syntactic constraints defined by regular expressions. The method constructs an analytic score to estimate the probability that a latent state decodes to a valid string and uses its gradient to steer sampling without auxiliary classifiers. In evaluations on 180 regular-expression constraints over JSON and natural-language benchmarks, Diffinity achieved 68-96% constraint satisfaction with minimal perplexity cost, outperforming autoregressive constrained decoding in both constraint adherence and output quality.", "body_md": "# Computer Science > Machine Learning\n\n[Submitted on 12 Feb 2026 (\n\n[v1](https://arxiv.org/abs/2602.12468v1)), last revised 27 May 2026 (this version, v2)]# Title:Continuous Diffusion Models Can Obey Formal Syntax\n\n[View PDF](/pdf/2602.12468)\n\nAbstract: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[this http URL].\n\n## Submission history\n\nFrom: Jinwoo Kim [[view email](/show-email/da38629a/2602.12468)]\n\n**Thu, 12 Feb 2026 22:55:05 UTC (71 KB)**\n\n[[v1]](/abs/2602.12468v1)**[v2]** Wed, 27 May 2026 11:13:24 UTC (75 KB)\n\n### References & Citations\n\nLoading...\n\n# Bibliographic and Citation Tools\n\nBibliographic Explorer\n\n*(*[What is the Explorer?](https://info.arxiv.org/labs/showcase.html#arxiv-bibliographic-explorer))\nConnected Papers\n\n*(*[What is Connected Papers?](https://www.connectedpapers.com/about))\nLitmaps\n\n*(*[What is Litmaps?](https://www.litmaps.co/))\nscite Smart Citations\n\n*(*[What are Smart Citations?](https://www.scite.ai/))# Code, Data and Media Associated with this Article\n\nalphaXiv\n\n*(*[What is alphaXiv?](https://alphaxiv.org/))\nCatalyzeX Code Finder for Papers\n\n*(*[What is CatalyzeX?](https://www.catalyzex.com))\nDagsHub\n\n*(*[What is DagsHub?](https://dagshub.com/))\nGotit.pub\n\n*(*[What is GotitPub?](http://gotit.pub/faq))\nHugging Face\n\n*(*[What is Huggingface?](https://huggingface.co/huggingface))\nScienceCast\n\n*(*[What is ScienceCast?](https://sciencecast.org/welcome))# Demos\n\n# Recommenders and Search Tools\n\nInfluence Flower\n\n*(*[What are Influence Flowers?](https://influencemap.cmlab.dev/))\nCORE Recommender\n\n*(*[What is CORE?](https://core.ac.uk/services/recommender))\nIArxiv Recommender\n\n*(*[What is IArxiv?](https://iarxiv.org/about))# arXivLabs: experimental projects with community collaborators\n\narXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.\n\nBoth individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.\n\nHave an idea for a project that will add value for arXiv's community? [ Learn more about arXivLabs](https://info.arxiv.org/labs/index.html).", "url": "https://wpnews.pro/news/continuous-diffusion-models-can-obey-formal-syntax", "canonical_source": "https://arxiv.org/abs/2602.12468", "published_at": "2026-05-29 06:55:57+00:00", "updated_at": "2026-05-29 07:16:23.256663+00:00", "lang": "en", "topics": ["machine-learning", "large-language-models", "generative-ai", "natural-language-processing", "ai-research"], "entities": ["Diffinity", "PLAID"], "alternates": {"html": "https://wpnews.pro/news/continuous-diffusion-models-can-obey-formal-syntax", "markdown": "https://wpnews.pro/news/continuous-diffusion-models-can-obey-formal-syntax.md", "text": "https://wpnews.pro/news/continuous-diffusion-models-can-obey-formal-syntax.txt", "jsonld": "https://wpnews.pro/news/continuous-diffusion-models-can-obey-formal-syntax.jsonld"}}