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

2026-05-15 · Source: cs.CL updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Software Development & Engineering · Depth: Expert, extended

Summary

This work introduces Manta-LM, a novel language generation framework that redefines text generation as a stochastic optimal control problem. It provides a unified theoretical perspective to analyze autoregressive (AR) and diffusion models, explaining their limitations like the Efficiency-Fidelity Paradox and Irreversibility Error Propagation through concepts such as trajectory singularity and adjoint state vanishing. Manta-LM addresses these issues by approximating the Hamilton-Jacobi-Bellman (HJB) equation, yielding an optimal policy that functions as a closed-loop controller. It employs Flow Matching as an optimal trajectory solver within a rectified latent control space, enabling its Global Integral Operator to approximate the global vector field. This approach allows Manta-LM to achieve high-fidelity text generation with efficient, low-cost parallel sampling, demonstrating strong performance on language modeling and conditional generation tasks, along with improved stability, efficiency, and controllability.

Key takeaway

For research scientists developing next-generation language models, Manta-LM offers a robust, mathematically grounded alternative to traditional AR and diffusion models. By reframing generation as an optimal control problem, you can overcome limitations like serial bottlenecks and error propagation. Consider adopting manifold rectification and flow matching techniques to achieve superior fidelity, efficiency, and controllability in tasks such as long-form infilling and self-correction, which are challenging for causal models.

Key insights

Language generation can be optimized as a stochastic control problem using rectified latent spaces and flow matching.

Principles

• Optimal control requires closed-loop feedback.
• Smooth geodesic flow minimizes transport energy.
• Manifold rectification reduces topological stiffness.

Method

Manta-LM uses a regularized VAE for manifold rectification, then applies Flow Matching to approximate the HJB equation, learning a vector field as a closed-loop controller via a Transformer-based global integral operator.

In practice

• Use VAEs to create smooth, locally Euclidean latent spaces.
• Apply Flow Matching for efficient, parallel text generation.
• Employ Transformers as global integral operators for control.

Topics

• Stochastic Optimal Control
• Language Generation
• Diffusion Language 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 cs.CL updates on arXiv.org.