GEM compares the student’s velocity prediction with a frozen teacher under target and benign anchor prompts. Its contrastive loss balances distance to the anchor against weighted distance to the target.
01 / Abstract
Abstract
Multimodal generators can reproduce harmful, impersonating, or copyrighted concepts. As image synthesis shifts from U-Net diffusion systems toward rectified-flow transformers, safeguards need to move with it. GEM introduces a concept-erasure objective for rectified-flow models that combines teacher-driven attraction toward benign behavior with repulsion from an unwanted concept. It connects trajectory-based unlearning ideas from Generative Flow Networks with flow-matching supervision, suppressing a chosen concept while preserving unrelated generation capabilities.
02 / Contributions
Contributions
01
Trajectory-based flow matching
Formulates trajectory-level unlearning signals as teacher-guided flow-matching supervision.
02
Geometric guidance
Combines attraction toward benign generation and repulsion from the target concept as a single velocity-space objective.
03
Concept erasure in rectified-flow models
Suppresses selected concepts in rectified-flow transformers while retaining the model’s broader generative behavior.
03 / Qualitative results
Generations before and after GEM
Compare five generations before and after GEM. Select a concept to bring it forward, then drag its divider to reveal the erased model output. Each comparison moves independently.
After GEM
Drag each image divider independently
Base FLUX
↔
Erasure target · 01 / 05bloody gore
04 / Objective
GEM in velocity space
Each arrow is a predicted change to the same noisy image representation at one timestep. Distances between these velocity predictions define GEM’s loss.
Zero-loss region L = 0.5, 1, 1.5, 2 Boundary: d₊ = ηd₋
Red contours connect equal positive loss. Fainter lines extend beyond the labeled values.Drag a tip · Arrow keys to move · Shift for larger steps
L = max(0, d₊ − η d₋)
Distance to anchor d₊
Weighted target distance η d₋
Positive lossL = 1.03
05
η = 1: zero loss on the anchor side of the perpendicular bisector.
Target
Frozen teacher · concept prompt
Anchor
Frozen teacher · benign anchor prompt
Student
Edited model · concept prompt
Both views show a two-dimensional slice at one latent and timestep; height in 3D represents loss. With clipping enabled, increasing η expands the zero-loss region. Turn clipping off to inspect the signed term. GEM trains over several early trajectory steps in parallel. Method and objective, Eqs. 13–14 ↗
05 / Citation
Citation
Grebe, J. H., Braun, T., Rohrbach, A., & Rohrbach, M. (2026). GEM: Geometric Erasure by Contrastive Velocity Matching in Rectified Flows. Forty-third International Conference on Machine Learning.
BibTeX+
@inproceedings{grebe2026gem,
title = {{GEM}: Geometric Erasure by Contrastive Velocity Matching in Rectified Flows},
author = {Jonas Henry Grebe and Tobias Braun and Anna Rohrbach and Marcus Rohrbach},
booktitle = {Forty-third International Conference on Machine Learning},
year = {2026},
url = {https://openreview.net/forum?id=NBMCwxTRSA}
}