aiqbench analysis
ReSFlow addresses a key bottleneck in discrete generative modeling by enforcing geodesic trajectories on statistical manifolds, enabling high-quality one-step generation instead of costly multi-step integration. By aligning flow paths with intrinsic Riemannian geometry, the method significantly reduces inference latency while maintaining fidelity across images, text, and biological data. This advancement represents a theoretical and practical leap in the efficiency of continuous normalizing flows for categorical data.
ReSFlow: Rectifying Categorical Flows on Statistical Manifolds for One-Step Generation
arXiv:2610.13225v1 Announce Type: new Abstract: Generative modeling for discrete data has been significantly advanced by learning continuous vector fields on the statistical manifolds to transport simple priors to target discrete distributions. However, because these continuous-time flows are not constrained to follow geodesics on the statistical manifold, thereby requiring multi-step numerical integration for simulation and leading to substantial computational costs during inference. In this work, drawing inspiration from the "straight and fast" properties of Rectified Flow in continuous Euclidean space, we propose the Rectified Statistical Flow (ReSFlow) model, which enables one-step categorical generation on statistical manifolds by explicitly learning geodesic trajectories that adhere to the intrinsic Riemannian geometry. By rectifying the flow on the statistical manifold, we theoretically guarantee that trajectories between prior and target distributions approximate geodesics. This rectification significantly reduces the transport cost by aligning the learned trajectories directly along geodesics on the statistical manifold, allowing the model to map pure noise to target discrete data in a single step. Through extensive experiments on diverse real-world generative tasks, ranging from image and text to biological domains, we demonstrate ReSFlow's superior one-step generation quality, which truly embodies geodesically optimal and rapid categorical generation. Our code is available at https://github.com/xiaohuanjia/ReSFlow.
Abstract:Generative modeling for discrete data has been significantly advanced by learning continuous vector fields on the statistical manifolds to transport simple priors to target discrete distributions. However, because these continuous-time flows are not constrained to follow geodesics on the statistical manifold, thereby requiring multi-step numerical integration for simulation and leading to substantial computational costs during inference. In this work, drawing inspiration from the "straight and fast" properties of Rectified Flow in continuous Euclidean space, we propose the Rectified Statistical Flow (ReSFlow) model, which enables one-step categorical generation on statistical manifolds by explicitly learning geodesic trajectories that adhere to the intrinsic Riemannian geometry. By rectifying the flow on the statistical manifold, we theoretically guarantee that trajectories between prior and target distributions approximate geodesics. This rectification significantly reduces the transport cost by aligning the learned trajectories directly along geodesics on the statistical manifold, allowing the model to map pure noise to target discrete data in a single step. Through extensive experiments on diverse real-world generative tasks, ranging from image and text to biological domains, we demonstrate ReSFlow's superior one-step generation quality, which truly embodies geodesically optimal and rapid categorical generation. Our code is available at this https URL.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2610.13225 [cs.LG]
(or arXiv:2610.13225v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.13225 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 293 words
Related coverage
Inference meta-monitoring for Amazon SageMaker AI endpoints with Amazon Quick
AWS · Jul 30, 2026
Computational and Statistical Guarantees of the \textit{c}-Rectified flow
arXiv · Aug 4, 2026
SDFlow: Similarity-Driven Flow Matching for Time Series Generation
arXiv · Oct 7, 2026
Generative Modeling of Discrete Data Using Geometric Latent Subspaces
arXiv · Sep 28, 2026