标题： $α$-Flow：连续状态离散流匹配模型的统一框架 显示英文标题

标题： $α$-Flow: A Unified Framework for Continuous-State Discrete Flow Matching Models

摘要： 近期的努力已将流匹配框架扩展到离散生成建模领域。 一类模型直接处理连续概率而非离散标记，我们通常称其为连续状态离散流匹配（CS-DFM）。 现有的 CS-DFM 模型在表示方法和几何假设上存在显著差异。 本文提出了一种统一的 CS-DFM 框架，在此框架下，现有变体可以被理解为作用于概率的不同$\alpha$表示上。 基于信息几何理论，我们引入了$\alpha$-Flow，这是一种遵循统计流形典型$\alpha$几何结构的 CS-DFM 模型族，并展示了其在最小化广义动能方面的最优性。 从理论上讲，我们证明了$\alpha$-Flow 的流匹配损失为离散负对数似然提供了统一的变分界。 我们在各种离散生成领域全面评估了$\alpha$-Flow 的不同实例，以展示它们在离散生成建模中的有效性，包括从未被探索过的中间值几何。 $\alpha$-Flow 在图像和蛋白质序列生成方面显著优于其离散状态对应物，并且在语言建模中更好地捕捉了熵。 显示英文摘要

摘要： Recent efforts have extended the flow-matching framework to discrete generative modeling. One strand of models directly works with the continuous probabilities instead of discrete tokens, which we colloquially refer to as Continuous-State Discrete Flow Matching (CS-DFM). Existing CS-DFM models differ significantly in their representations and geometric assumptions. This work presents a unified framework for CS-DFM models, under which the existing variants can be understood as operating on different $\alpha$-representations of probabilities. Building upon the theory of information geometry, we introduce $\alpha$-Flow, a family of CS-DFM models that adheres to the canonical $\alpha$-geometry of the statistical manifold, and demonstrate its optimality in minimizing the generalized kinetic energy. Theoretically, we show that the flow matching loss for $\alpha$-flow establishes a unified variational bound for the discrete negative log-likelihood. We comprehensively evaluate different instantiations of $\alpha$-flow on various discrete generation domains to demonstrate their effectiveness in discrete generative modeling, including intermediate values whose geometries have never been explored before. $\alpha$-flow significantly outperforms its discrete-state counterpart in image and protein sequence generation and better captures the entropy in language modeling.