Geometric Erasure by Contrastive Velocity Matching in Rectified Flows

2026-05-28

AI Summary

This work addresses the pressing risks of malicious content synthesis, deepfakes, and copyright infringement in Rectified Flow–based multimodal generative models, where existing approaches lack effective mechanisms for concept erasure. To this end, we propose GEM, a novel framework that achieves efficient concept unlearning within Rectified Flow for the first time. GEM integrates a trajectory-driven forgetting mechanism with teacher-guided erasure, introducing attraction–repulsion signals into flow matching to formulate a unified geometrically guided objective. By combining contrastive velocity matching with trajectory optimization, our method precisely suppresses harmful concepts while substantially preserving the model’s high-fidelity generation capability for non-target content. Furthermore, we establish a theoretical connection between trajectory-driven forgetting and teacher-guided erasure, providing principled insights into the underlying dynamics of concept removal.

Abstract

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.

Problem

• concept erasure
• Rectified Flow
• generative models
• harmful content
• copyright infringement

Innovation

• concept erasure
• Rectified Flow
• contrastive velocity matching
• teacher-guided unlearning
• geometric guidance