Diffusion Language Models as Open Quantum Systems

Abstract: Diffusion LLMs generate text by reversing a classical diffusion process over token sequences. We show that their continuous-time forward and reverse dynamics can be embedded in the framework of open quantum systems, which describes quantum systems interacting with their environment. This connection provides a basis for extending diffusion sampling to superpositions of sentence states and for modifying the underlying generation dynamics. We construct a $τ$-leaping unraveling scheme that simulates stochastic trajectories of these states while updating multiple token positions at each step. This enables generation conditioned on superposed prompts or thoughts, which we call Superposition of Prompts (SoP) and Superposition of Thoughts (SoT). The same formulation yields Quantum-Inspired Remasking (QIR): perturbing the masked-diffusion dynamics produces a confidence-based rule for revising previously generated tokens. Experiments with pretrained diffusion LLMs show that superposition-based generation can retain information from conditioning components not selected at the final measurement, while QIR improves LLM-assessed text quality when applied at an appropriate stage of generation.