Generative modeling for discrete data has recently progressed by learning continuous vector fields on statistical manifolds to transport simple priors to target discrete distributions.
However, these continuous‑time flows are not constrained to follow geodesics on the statistical manifold, which forces multi‑step numerical integration during inference and incurs heavy computational cost.
Inspired by the “straight and fast” property of Rectified Flow in Euclidean space, we propose the Rectified Statistical Flow (ReSFlow) model. It explicitly learns trajectories that respect the intrinsic Riemannian geometry, enabling one‑step categorical generation on the statistical manifold.
By rectifying the flow on the statistical manifold we theoretically guarantee that the path between prior and target approximates a geodesic:$$L(\gamma)=\int_0^1 \sqrt{g_{\gamma(t)}(\dot\gamma(t),\dot\gamma(t))}\,dt$$. This alignment dramatically reduces transport cost, allowing the model to map pure noise directly to target discrete data in a single step.
Extensive experiments on diverse real‑world generative tasks—including images, text, and biological data—show that ReSFlow achieves superior one‑step generation quality, truly embodying geodesically optimal and rapid categorical generation.
The code is released at https://github.com/xiaohuanjia/ReSFlow
Review: ReSFlow integrates Riemannian geometry into the core of discrete generation, offering a theoretically grounded and practically efficient one‑step solution that advances high‑speed discrete modeling.