Newest papers

Binary Discrete Diffusion: Candidate-Set Diffusion for Logic and Planning Tasks

Rodrigo Casado Noguerales, Dimitri von Rütte, Bernhard Schölkopf, Thomas Frank Hofmann, Aran Raoufi · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28543 · cited by 0 works (OpenAlex) · open-access PDF

German

Diskrete Budgetherausgabe-Modelle dementieren iterativ eine laute Reihenfolge kategorischer Daten wie Text, wodurch jede Order-Generation mit selbstkorrigierenden und effektiven Füllfähigkeiten erlaubt wird. Dies macht sie zu vielversprechenden Kandidaten für Argumentation, Planung und begrenzte Generationsaufgaben wie Codierung und Mathematik. Doch maskierte und einheitliche Diffusion löscht die Identität eines Tokens in einem einzigen Korruptionsereignis, so dass ihre lauten Zustände nicht explizit teilweise gelöste Unsicherheiten darstellen können, in denen mehrere Alternativen plausibel bleiben. Wir schließen diese Lücke mit Binary Discrete Diffusion, einer Familie von kontinuierlichen, diskreten Diffusionsprozessen, deren geräuschiger Zustand eine Reihe von Kandidaten-

Machine translation (Meta M2M100); the English original follows.

Abstract

Discrete diffusion models iteratively denoise a noisy sequence of categorical data such as text, enabling any-order generation with self-correction and in-filling capabilities. This makes them promising candidates for reasoning, planning, and constrained-generation tasks like coding and math. Yet masked and uniform diffusion erase a token's identity in a single corruption event, so their noisy states cannot explicitly represent partially resolved uncertainty in which several alternatives remain plausible. We close this gap with Binary Discrete Diffusion, a family of continuous-time discrete-diffusion processes whose noisy state is a set of candidate tokens per position, represented as a binary membership vector. Binary diffusion changes candidate sets through additions and removals, allowing information to be lost and recovered gradually while the diffusion state itself represents partial uncertainty. On Sudoku-Extreme, Boxoban, and graph coloring, the symmetric formulation of binary diffusion consistently outperforms strong, well-tuned masked and uniform baselines under matched architectures and controlled training, sampling, and tuning budgets, with its largest gains on the hardest instances, while remaining competitive on language modeling (Text8, TinyStories, OpenWebText). These results support candidate sets as an effective intermediate representation for iterative reasoning and show that the corruption kernel can materially change the computation learned by the reverse model.

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Topics: Binary number, Categorical variable, Algorithm, Computer science, Computation, Theoretical computer science

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