Language Generation as Optimal Control: Closed-Loop Diffusion in Latent Control Space

2026-05-14 · Source: Computation and Language · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

A new framework redefines language generation as a stochastic optimal control problem, offering a unified theoretical lens for analyzing autoregressive and diffusion models. This perspective explains limitations like the Efficiency-Fidelity Paradox and Irreversibility Error Propagation through concepts such as trajectory singularity and adjoint state vanishing. To overcome these, the authors approximate the Hamilton-Jacobi-Bellman (HJB) equation's solution, deriving an optimal policy that functions as a closed-loop controller. By using Flow Matching as an optimal trajectory solver in a rectified latent control space, their Manta-LM model, equipped with a Global Integral Operator, approximates the global vector field. This approach enables high-fidelity text generation with efficient, low-cost parallel sampling, demonstrating strong empirical performance in language modeling and conditional generation tasks.

Key takeaway

For research scientists developing advanced language models, this optimal control framework offers a novel theoretical foundation to address persistent challenges like efficiency and fidelity. You should investigate integrating Hamilton-Jacobi-Bellman equation approximations and Flow Matching techniques into your model architectures to achieve more stable, efficient, and controllable text generation, potentially overcoming limitations seen in current autoregressive and diffusion models.

Key insights

Language generation can be reframed as a stochastic optimal control problem to address model limitations.

Principles

• Optimal control unifies AR and diffusion models.
• HJB equation approximation yields optimal policies.

Method

Flow Matching solves optimal trajectories in rectified latent control space, enabling Manta-LM's Global Integral Operator to approximate global vector fields for efficient, high-fidelity generation.

In practice

• Apply optimal control to language generation.
• Utilize Flow Matching for trajectory solving.

Topics

• Stochastic Optimal Control
• Language Generation
• Diffusion Models
• Autoregressive Models
• Flow Matching

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, NLP Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Computation and Language.