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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

Indonesian

Model distribusi diskret secara iteratif mendeskripsikan urutan berisik dari data kategoris seperti teks, memungkinkan generasi setiap urutan dengan kemampuan self-correction dan in-filling. Ini membuat mereka kandidat yang menjanjikan untuk alasan, perencanaan, dan tugas-tugas generasi terbatas seperti pengkodean dan matematika. Namun, distribusi tertutup dan seragam menghapus identitas token dalam peristiwa korupsi tunggal, sehingga negara-negara mereka yang berisik tidak dapat secara eksplisit mewakili ketidakpastian yang terselesaikan secara parsial di mana beberapa alternatif tetap dapat diandalkan. Kami menutup kesenjangan ini dengan distribusi diskret biner, keluarga proses distribusi diskret yang berkelanjutan pada waktu yang berkelanjutan, di mana negara-negara yang tidak tertutup adalah set terbesar dari token kandidat per posisi,

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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