Discrete MeanFlow: One-Step Generation for Discrete State Spaces
Researchers have developed a novel technique called Discrete MeanFlow to analyze changes in discrete state spaces in a single phase. This method contrasts with traditional continuous MeanFlow, which tracks average velocities over time. Instead, Discrete MeanFlow focuses on shifts in probability among a limited range of states. The approach utilizes the conditional transition kernel from a continuous-time Markov chain to derive a mean discrete transition rate that reflects the average variations in state probabilities over a specific duration. The team established a correlation between this discrete rate and the Markov chain’s instantaneous generator using the Kolmogorov forward equation.
Key facts
- Discrete MeanFlow enables one-step generation in discrete state spaces.
- It replaces point motion with transport of probability mass over finite states.
- The key object is the conditional transition kernel of a CTMC.
- A mean discrete rate measures average change in transition probability over a time interval.
- A Discrete MeanFlow identity relates the finite-interval rate to the instantaneous CTMC generator.
- The Kolmogorov forward equation replaces the spatial chain rule of continuous MeanFlow.
- The method parameterizes the transition kernel directly.
- The paper is available on arXiv under ID 2605.12805.
Entities
Institutions
- arXiv