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[Submitted on 1 Oct 2026] Title:Exploring the Design Space of Permutation Diffusion LLMs View a PDF of the paper titled Exploring the Design Space of Permutation Diffusion LLMs, by Zhe Xu and 18 other authors View PDF HTML (experimental) Abstract:Permutation generation with language models requires both text-conditioned ranking and a global one-to-one assignment between candidates and output positions. We study this problem through three diffusion-LLM parameterizations: hard-assignment prediction over shuffled candidate-index sequences, soft-assignment prediction over doubly stochastic matrices, and direct ordering-score prediction followed by sorting. The three families place permutation constraints at different stages of prediction and decoding and therefore support different training objectives and sampling procedures. We evaluate these designs on recommendation reranking across three Amazon domains with candidate sets of size 10 and 20. At one function evaluation, the hard- and soft-assignment variants achieve Recall@1 comparable to a constrained masked-diffusion baseline, whereas direct ordering-score prediction guarantees valid permutations without Hungarian assignment or Sinkhorn normalization. Additional function evaluations do not consistently improve ranking quality, and their effect depends strongly on the state representation and training objective. These results show that corruption, prediction parameterization, objective, and decoder should be designed jointly for permutation diffusion with language-model denoisers. Subjects: Computation and Language (cs.CL); Artificial Intelligence (cs.AI); Machine Learning (cs.LG) Cite as: arXiv:2610.20635 [cs.CL] (or arXiv:2610.20635v1 [cs.CL] for this version) https://doi.org/10.48550/arXiv.2610.20635 arXiv-issued DOI via DataCite Submission history From: Zhe Xu [view email] [v1] Thu, 1 Oct 2026 03:39:40 UTC (472 KB) Full-text links: Access Paper: View a PDF of the paper titled Exploring the Design Space of Permutation Diffusion LLMs, by Zhe Xu and 18 other authors View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.CL new | recent | 2026-10 Change to browse by: cs cs.AI cs.LG References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both 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. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)