将语言生成视为最优控制，实现高效高质并行生成。
Language Generation as Optimal Control: Closed-Loop Diffusion in Latent Control Space
- 把文本生成建模为最优控制问题，统一解释自回归与扩散模型缺陷。
- 通过流匹配求解，实现高质量且可并行采样的全局控制策略。
- 适合追求生成效率与可控性的研究者或工业应用开发人员。
本文将语言生成重新构想为随机最优控制问题，提供统一的理论视角，分析自回归与扩散模型的局限性（效率-保真度悖论、不可逆误差传播、优化可处理性与保真度），归因于轨迹奇异、伴随状态消失和梯度缺失的组合。为解决这些问题，我们近似求解哈密顿-雅可比-贝尔曼（HJB）方程，得到一种闭环控制器。为避免直接求解高维非线性偏微分方程的不可行性，我们在修正的潜在控制空间中使用流匹配作为最优轨迹求解器。由此构建的Manta-LM结合全局积分算子，逼近全局向量场，实现了高保真文本生成与低开销并行采样的统一。实验表明，该方法在语言建模与条件生成任务中表现优异，具备更强稳定性、效率与可控性。
原文摘要 · Abstract (English)
This work reformulates language generation as a stochastic optimal control problem, providing a unified theoretical perspective to analyze autoregressive and diffusion models and explain their limitations (Efficiency-Fidelity Paradox, Irreversibility Error Propagation, Optimization Tractability and Fidelity) in terms of combination of trajectory singularity, adjoint state vanishing, and gradient absence. To address these issues, we approximate the solution to the Hamilton-Jacobi-Bellman (HJB) equation, yielding an optimal policy that acts as a closed-loop controller. To bypass the intractability of directly solving the HJB PDE, we employ Flow Matching as the optimal trajectory solver within the rectified latent control space. This allows our Manta-LM with Global Integral Operator to approximate the global vector field, effectively realizing a model that simultaneously achieves high-fidelity text generation and efficient, low-cost parallel sampling. Empirically, our method achieves strong performance on language modeling and conditional generation tasks, while exhibiting improved stability, efficiency, and controllability.
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