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

Chinese

二进制扩散模型重复地消除类别数据的噪音序列,如文本,允许任何命令生成具有自我纠正和有效填充能力。这使他们成为有前途的候选人来推理,规划和限制生成任务,如编码和数学。然而,掩盖和统一扩散在一个单一的腐败事件中删除一个代币的身份,所以他们的噪音状态不能明确表示部分解决的不确定性,其中几个替代品仍然是可信的。我们用二进制扩散,一个连续时间的分散扩散过程的家族,缩小了这个差距,而二进制扩散过程则是连续的。在中间状态中,噪音是每位候选人代币的最大集合,以二进制成员符号为代表。这些二进制扩

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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