Discrete MeanFlow: One-Step Generation via Conditional Transition Kernels

MeanFlow enables one-step generation in continuous spaces by learning an average velocity over a time interval rather than the instantaneous velocity field of flow matching. However, discrete state spaces do not have smooth trajectories or spatial derivatives, so the continuous formulation does not directly apply. We introduce Discrete MeanFlow, which replaces the motion of a point with the transport of probability mass over finite states. Our key object is the conditional transition kernel of a continuous-time Markov chain (CTMC), from which we define a mean discrete rate that measures the average change in transition probability over a time interval. We prove a Discrete MeanFlow identity that relates this finite-interval rate to the instantaneous CTMC generator at the endpoint, with the Kolmogorov forward equation replacing the spatial chain rule of continuous MeanFlow. Based on this identity, we parameterize the transition kernel directly using a boundary-by-construction design that guarantees valid probability outputs and exact boundary conditions without auxiliary losses. Since the learned kernel is itself a probability distribution, generation reduces to a single forward pass followed by one categorical draw meaning no iterative denoising, ODE integration, or multi-step refinement is required. We validate the framework on exact finite-state Markov chains, where the learned kernel recovers the analytical ground truth to high precision, and on factorized synthetic sequence generation tasks with varying alphabet sizes and sequence lengths.

Improving Multi-turn Task Completion in Task-Oriented Dialog Systems via Prompt Chaining and Fine-Grained Feedback

Task-oriented dialog (TOD) systems facilitate users in accomplishing complex, multi-turn tasks through natural language. While traditional approaches rely on extensive fine-tuning and annotated data for each domain, instruction-tuned large language models (LLMs) offer a more flexible alternative. However, LLMs struggle to reliably handle multi-turn task completion, particularly with accurately generating API calls and adapting to new domains without explicit demonstrations. To address these challenges, we propose RealTOD, a novel framework that enhances TOD systems through prompt chaining and fine-grained feedback mechanisms. Prompt chaining enables zero-shot domain adaptation via a two-stage prompting strategy, eliminating the need for human-curated demonstrations. Meanwhile, the fine-grained feedback mechanism improves task completion by verifying API calls against domain schemas and providing precise corrective feedback when errors are detected. We conduct extensive experiments on the SGD and BiTOD benchmarks using four LLMs. RealTOD improves API accuracy, surpassing AutoTOD by 37.74% on SGD and SimpleTOD by 11.26% on BiTOD. Human evaluations further confirm that LLMs integrated with RealTOD achieve superior task completion, fluency, and informativeness compared to existing methods.