# GEM: Geometric Erasure by Contrastive Velocity Matching in Rectified Flows

arXiv: https://arxiv.org/abs/2606.00140 · HTML: https://mlsanity.com/paper/2606.00140/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Robustness, privacy and adversarial aspects, one of 14 directions in Diffusion models.
- Builds on 40 of its 53 references that are in the map.
- First posted on arXiv 29 May 2026.

## Placed in

- Diffusion models / [Robustness, privacy and adversarial aspects](https://mlsanity.com/diffusion/robustness-privacy-and-adversarial-aspects/)
- LLM safety and security / [Vision-language and text-to-image safety](https://mlsanity.com/safety/vision-language-and-text-to-image-safety/)

## Builds on (most cited first, 30 of 40)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [FLUX.1 Kontext: Flow Matching for In-Context Image Generation and Editing in Latent Space](https://mlsanity.com/paper/2506.15742/) (2025)
- [Flow-GRPO: Training Flow Matching Models via Online RL](https://mlsanity.com/paper/2505.05470/) (2025)
- [Erasing Concepts from Diffusion Models](https://mlsanity.com/paper/2303.07345/) (2023)
- [Safe Latent Diffusion: Mitigating Inappropriate Degeneration in Diffusion Models](https://mlsanity.com/paper/2211.05105/) (2022)
- [Unified Concept Editing in Diffusion Models](https://mlsanity.com/paper/2308.14761/) (2023)
- [Ablating Concepts in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.13516/) (2023)
- [MACE: Mass Concept Erasure in Diffusion Models](https://mlsanity.com/paper/2403.06135/) (2024)
- [Forget-Me-Not: Learning to Forget in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.17591/) (2023)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [Red-Teaming the Stable Diffusion Safety Filter](https://mlsanity.com/paper/2210.04610/) (2022)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Ring-A-Bell! How Reliable are Concept Removal Methods for Diffusion Models?](https://mlsanity.com/paper/2310.10012/) (2023)
- [MMA-Diffusion: MultiModal Attack on Diffusion Models](https://mlsanity.com/paper/2311.17516/) (2023)
- [Prompting4Debugging: Red-Teaming Text-to-Image Diffusion Models by Finding Problematic Prompts](https://mlsanity.com/paper/2309.06135/) (2023)
- [One-Dimensional Adapter to Rule Them All: Concepts, Diffusion Models and Erasing Applications](https://mlsanity.com/paper/2312.16145/) (2023)
- [Defensive Unlearning with Adversarial Training for Robust Concept Erasure in Diffusion Models](https://mlsanity.com/paper/2405.15234/) (2024)
- [Can Machines Help Us Answering Question 16 in Datasheets, and In Turn Reflecting on Inappropriate Content?](https://mlsanity.com/paper/2202.06675/) (2022)

## Built on by (most cited first, 2 of 2)

- [Obliviate: Erasing Concepts from Autoregressive Image Generation Models](https://mlsanity.com/paper/2606.28643/) (2026)
- [VETO: Towards Protecting Images From Frontier AI Editing](https://mlsanity.com/paper/2607.27292/) (2026)

## Abstract (arXiv)

While the rapid adoption of multimodal generative models offers immense potential, it has also increased the risks of harmful content synthesis, deepfakes, and copyright infringements. To address these challenges, concept erasure has emerged as a prospective safeguard. However, as the field gradually transitions from U-Net-based diffusion models to Rectified Flow Transformers, erasure research has struggled to keep pace. In this work, we introduce GEM, a simple but highly effective erasure framework for Rectified Flow models. As part of our contribution, we establish a principled bridge between trajectory-based unlearning grounded in Generative Flow Networks and classic teacher-guided erasure: we translate trajectory-based signals into a teacher-guided flow-matching setup that unifies the strengths of both paradigms. Concretely, a teacher provides complementary attraction and repulsion signals that we combine into a single geometric guidance objective, yielding targeted suppression of unwanted concepts while preserving benign generation. Our code is available at https://github.com/multimodal-ai-lab/GEM.