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This research advances one-step generation by addressing the geometric constraints of non-Euclidean data spaces, moving beyond standard additive updates to derive geometry-aware fields. The study demonstrates that optimal field selection is task-dependent, offering a practical framework for improving inference speed on structured datasets without sacrificing distributional fidelity.
One-Step Generation via Riemannian Wasserstein Gradient Flows
arXiv:2610.04454v1 Announce Type: new Abstract: Recently, Drifting Models and Wasserstein Gradient Flows have attracted substantial attention because they move iterative distributional refinement to training and amortize it into a generator, enabling fast inference. However, existing formulations have been developed largely for continuous Euclidean domains, such as image spaces, where particles admit unconstrained additive updates. On constrained spaces, these updates can leave the valid domain or ignore its geometry, making them unsuitable targets for training. Recent work has adapted updates to these spaces, but has focused on particular fields or offered limited empirical comparison. We derive and compare several geometry-aware fields within a common training framework for one-step generators. We test the method on data with different structures and obtain competitive one-step results in each setting. The best-performing field varies by task, showing why the choice of objective matters in practice.
Abstract:Recently, Drifting Models and Wasserstein Gradient Flows have attracted substantial attention because they move iterative distributional refinement to training and amortize it into a generator, enabling fast inference. However, existing formulations have been developed largely for continuous Euclidean domains, such as image spaces, where particles admit unconstrained additive updates. On constrained spaces, these updates can leave the valid domain or ignore its geometry, making them unsuitable targets for training. Recent work has adapted updates to these spaces, but has focused on particular fields or offered limited empirical comparison. We derive and compare several geometry-aware fields within a common training framework for one-step generators. We test the method on data with different structures and obtain competitive one-step results in each setting. The best-performing field varies by task, showing why the choice of objective matters in practice.
Machine Learning (cs.LG)
arXiv:2610.04454 [cs.LG]
(or arXiv:2610.04454v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.04454 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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