Language Generation as Optimal Control: Closed-Loop Diffusion in Latent Control Space
For researchers in language generation, this work provides a unified theoretical framework and a practical method that addresses key limitations of existing models, though the empirical gains are not quantified with specific numbers.
This paper reformulates language generation as a stochastic optimal control problem, identifying limitations of autoregressive and diffusion models, and proposes a closed-loop controller via Flow Matching in latent control space. The method achieves high-fidelity text generation with efficient parallel sampling, showing strong performance on language modeling and conditional generation tasks.
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.