Signed Rectified Flow: Negativity-Controlled Generation

Abstract:We introduce Signed Rectified Flow (Signed RF), a generalization of Rectified Flow that targets the signed measure $\pi^{sign} = (1+\alpha)\pi^+ - \alpha\pi^-$, where $\alpha>0$, $\pi^+$ is the distribution to promote, and $\pi^-$ is the distribution to suppress. Although direct sampling from a signed measure is not well-defined, Signed RF induces a valid generative process that concentrates probability in regions where the signed measure is positive while provably excluding regions dominated by its negative component. It therefore provides a principled framework for incorporating negative information and exclusion constraints into generative modeling. We analyze the signed continuity equation underlying Signed RF and use a charged-particle interpretation to explain how negative mass forms exclusion barriers. This theory further motivates practical adaptive guidance algorithms. Across several applications, Signed RF improves the fidelity-diversity trade-off on ImageNet, reduces nearest-neighbor similarity in anti-memorization experiments, and reduces nudity induced by adversarial prompts in Stable Diffusion 3.5 while preserving CLIP and aesthetic scores.

Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV)

arXiv:2607.18516 [cs.LG]

(or arXiv:2607.18516v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.18516 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.