{"ID":2892020,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.15897","arxiv_id":"2507.15897","title":"ReDi: Rectified Discrete Flow","abstract":"Discrete Flow-based Models (DFMs) are powerful generative models for high-quality discrete data but typically suffer from slow sampling speeds due to their reliance on iterative decoding processes. This reliance on a multi-step process originates from the factorization approximation of DFMs, which is necessary for handling high-dimensional data. In this paper, we analyze the factorization approximation error using Conditional Total Correlation (TC), and reveal its dependence on the coupling. To address the challenge of efficient few-step generation, we propose Rectified Discrete Flow (ReDi), a novel iterative method that reduces the underlying factorization error (measured as Conditional TC) by rectifying the coupling between source and target distributions. We theoretically prove that each ReDi step guarantees a monotonic decreasing Conditional TC, ensuring its convergence. Empirically, ReDi significantly reduces Conditional TC and enables few-step generation. Moreover, we demonstrate that the rectified couplings are well-suited for training efficient one-step models on image generation. ReDi offers a simple and theoretically grounded approach for tackling the few-step challenge, providing a new perspective on efficient discrete data synthesis. Code is available at https://github.com/Ugness/ReDi_discrete.","short_abstract":"Discrete Flow-based Models (DFMs) are powerful generative models for high-quality discrete data but typically suffer from slow sampling speeds due to their reliance on iterative decoding processes. This reliance on a multi-step process originates from the factorization approximation of DFMs, which is necessary for hand...","url_abs":"https://arxiv.org/abs/2507.15897","url_pdf":"https://arxiv.org/pdf/2507.15897v2","authors":"[\"Jaehoon Yoo\",\"Wonjung Kim\",\"Seunghoon Hong\"]","published":"2025-07-21T01:18:44Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"stat.ML\"]","methods":"[]","has_code":false,"code_links":[{"ID":611944,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2892020,"paper_url":"https://arxiv.org/abs/2507.15897","paper_title":"ReDi: Rectified Discrete Flow","repo_url":"https://github.com/Ugness/ReDi_discrete","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}