Language Generation as Optimal Control: Closed-Loop Diffusion in Latent Control Space
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 with...
| Authors | ZiYi Dong, Yuliang Huang, Weijian Deng et al. |
|---|---|
| Primary category | cs.CL |
| Published | 14 May 2026 |
| Last updated at source | 7 June 2026 |
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