Signed Rectified Flow: Negativity-Controlled Generation

תקציר מקורי באנגליתarXiv:2607.18516v1 Announce Type: new 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 i