# Signed Rectified Flow: Negativity-Controlled Generation

arXiv: https://arxiv.org/abs/2607.18516 · HTML: https://mlsanity.com/paper/2607.18516/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 66 of its 80 references that are in the map.
- First posted on arXiv 20 Jul 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 66)

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- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
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- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Diffusion Model Alignment Using Direct Preference Optimization](https://mlsanity.com/paper/2311.12908/) (2023)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think](https://mlsanity.com/paper/2410.06940/) (2024)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)

## Abstract (arXiv)

We introduce Signed Rectified Flow (Signed RF), a generalization of Rectified Flow that targets the signed measure πsign = (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.