Signed Rectified Flow: Negativity-Controlled Generation

2026/07/20 by Runlong Liao, Baiyu Su, Lizhang Chen +1
#cs.LG #cs.CV

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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.

Citations

• Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think
• Extracting Training Data from Diffusion Models
• Affective Coherence Monitoring for Transformer-Based Language Models
• Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Models
• Building Normalizing Flows with Stochastic Interpolants
• Training language models to follow instructions with human feedback
• GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models
• Diffusion Models Beat GANs on Image Synthesis
• Neural Ordinary Differential Equations
• Improved Techniques for Training GANs

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• EMAG: Self-Rectifying Diffusion Sampling with Exponential Moving Average Guidance
• Flowification: Everything is a Normalizing Flow