01 / Key message
GEM: Geometric Erasure by Contrastive Velocity Matching in Rectified Flows
A geometric training objective that removes targeted concepts from rectified-flow generators while protecting benign behavior.
Contrastive velocity field
02 / Method
How it works
Observe the field
A teacher model exposes how the rectified-flow velocity changes with and without the target concept.
Contrast directions
Repulsive and attractive velocity signals identify a geometric direction away from the unwanted concept.
Match safely
The student follows the corrected velocity field while staying aligned with benign generation.
03 / 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.
04 / Contributions
What this adds
- 01
A bridge between paradigms
Recasts trajectory-level unlearning signals as teacher-guided flow matching, bringing two complementary approaches into one formulation.
- 02
Geometric guidance
Combines attraction toward benign generation and repulsion from the target concept as a single velocity-space objective.
- 03
Targeted intervention
Suppresses selected concepts in rectified-flow transformers while retaining the model’s broader generative behavior.
05 / Qualitative results
Concept erasure, seen directly
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.
GEM · safe variant
Drag each image divider independently
FLUX · unsafe baseErasure target · 01 / 05❌ bloody gore
GEM redirects the generation away from the bloody-gore erasure target.
06 / Interactive analysis
Geometry, not just suppression
GEM combines attraction and repulsion in velocity space, then applies that signal across the influential portion of a rectified-flow path.
Velocity-space objective
η = 1.0Pull toward safe dynamics, push away from the target
Current latent xtfixed
Teacher anchordpos · safe
Teacher targetdneg · unsafe
dpos
dneg
dpos − η · dneg
contrastive update
Higher η strengthens repulsion around the fixed teacher target; only the black combination changes.
GEM loss
max(0, d₊ − η · d₋)Trajectory supervision
One coherent pathSeveral influential states, one parallel pass
x₀loss
x₁loss
x₂loss
x₃loss
x₄loss
x₅
x₆
x₇
trajectory 1
x₂
trajectory 2
x₅
trajectory 3
x₃
trajectory 4
x₆
GEM samples one target trajectory and optimizes 5 consecutive states from it in parallel.
07 / 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}
}