Flow Matching with General Discrete Paths: A Kinetic-Optimal Perspective
This work addresses the problem of designing more flexible and effective discrete generative models for researchers and practitioners in machine learning, offering a novel framework that is not incremental but introduces a new perspective.
The paper tackles the limited design space of discrete generative models by introducing a method to use arbitrary discrete probability paths, optimizing symmetric kinetic energy to decouple probability and velocity. The approach outperforms existing mask constructions in text generation and enables domain-specific paths in visual tasks.
The design space of discrete-space diffusion or flow generative models are significantly less well-understood than their continuous-space counterparts, with many works focusing only on a simple masked construction. In this work, we aim to take a holistic approach to the construction of discrete generative models based on continuous-time Markov chains, and for the first time, allow the use of arbitrary discrete probability paths, or colloquially, corruption processes. Through the lens of optimizing the symmetric kinetic energy, we propose velocity formulas that can be applied to any given probability path, completely decoupling the probability and velocity, and giving the user the freedom to specify any desirable probability path based on expert knowledge specific to the data domain. Furthermore, we find that a special construction of mixture probability paths optimizes the symmetric kinetic energy for the discrete case. We empirically validate the usefulness of this new design space across multiple modalities: text generation, inorganic material generation, and image generation. We find that we can outperform the mask construction even in text with kinetic-optimal mixture paths, while we can make use of domain-specific constructions of the probability path over the visual domain.