Signed Rectified Flow: Negativity-Controlled Generation

2026-07-20

AI Summary

This work addresses the challenge of effectively incorporating negative constraints into generative models to suppress undesired sample regions. The authors propose Signed Rectified Flow, which introduces signed measures into the flow matching framework for the first time, modeling both positive and negative "masses" to guide the generation process: positive mass attracts probability flow toward target regions, while negative mass acts as a repulsive barrier to avoid undesirable content. Grounded in a signed continuity equation and inspired by analogies to charged particles, the method employs an adaptive guidance mechanism that provides theoretical guarantees for controllable generation. Experiments demonstrate that the approach improves the fidelity-diversity trade-off on ImageNet, reduces nearest-neighbor similarity in anti-memorization tasks, and effectively suppresses nudity induced by adversarial prompts in Stable Diffusion 3.5, all while preserving CLIP and aesthetic scores.

Abstract

We introduce Signed Rectified Flow (Signed RF), a generalization of Rectified Flow that targets the signed measure $π^{sign} = (1+α)π^+ - απ^-$, where $α>0$, $π^+$ is the distribution to promote, and $π^-$ 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.

Problem

• signed measure
• generative modeling
• exclusion constraints
• negative information
• Rectified Flow

Innovation

• Signed Rectified Flow
• signed measure
• negative information
• exclusion constraints
• adaptive guidance