# Signed Rectified Flow: Negativity-Controlled Generation Source: [Signed Rectified Flow: Negativity-Controlled Generation]() Collection index: [llms.txt]() Data updated: 2026-07-23T05:00:05.031Z Authors: Runlong Liao, Baiyu Su, Lizhang Chen, Qiang Liu Published: 2026-07-20T21:15:34.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()