Categorical Flow Maps

We introduce Categorical Flow Maps, a flow-matching method for accelerated few-step generation of categorical data via self-distillation. Building on recent variational formulations of flow matching and the broader trend towards accelerated inference in diffusion and flow-based models, we define a flow map towards the simplex that transports probability mass toward a predicted endpoint, yielding a parametrisation that naturally constrains model predictions. Since our trajectories are continuous rather than discrete, Categorical Flow Maps can be trained with existing distillation techniques, as well as a new objective based on endpoint consistency. This continuous formulation also automatically unlocks test-time inference: we can directly reuse existing guidance and reweighting techniques in the categorical setting to steer sampling toward downstream objectives. Empirically, we achieve state-of-the-art few-step results on images, molecular graphs, and text, with strong performance even in single-step generation.

We investigate the problem of generating discrete data through a diffusion process which is continuous. We show that, by reparameterising our prediction target based on the clean point of the diffusion, we can a model for cross-entropy denoising/prediction. Given that, we also show that it is possible to enable few-step training techniques, hitherto available to continuous data only. Empirically, we show good performance in the very few-step sample regime (down to one).