Background Gradients Shape Memorization in Flow Matching

2026-09-27

AI Summary

This study investigates how non-target background images influence the memorization and replication of targets in generative models via gradient dynamics. Building upon class-conditional flow matching, this work proposes a paired trajectory framework that establishes a geometric connection between background loss landscapes and target learning curvature through path integral curvature representations and parameter displacement isolation analysis, thereby revealing the intrinsic mechanisms by which intra-class data shape model behavior. Cross-dataset experiments confirm the causal role of background gradient responses. Notably, we find that after removing the target object, correcting only the parallel displacement preserves approximately 90% of the replication effect. These findings offer new perspectives for understanding target retention and replication behaviors in generative models.

Abstract

Repetition is closely associated with memorization in generative models, but how other training images affect the retention and copying of targets remains unclear. We study this question in class-conditioned flow matching, where images outside the target set form the background. At fixed target repetition and same-class background row count, replacing repeated same-class images with distinct images reduces the target extraction rate from 80.7% to 18.0%. To explain this effect, we develop a paired-trajectory framework that isolates target-induced parameter displacement and the background gradient response to it. This response has an exact path-integrated curvature representation, connecting background loss geometry to target learning. Reciprocal response transfer between repeated and distinct backgrounds changes target retention and copying in both directions, establishing the response's causal role. After target removal, the response correction parallel to the target-induced displacement preserves approximately 90% of the copying effects of full response transfer. Directly scaling the displacement also changes copying without further training. The post-removal copying effects of reciprocal transfer are reproduced across datasets and architectures. Together, these results identify the background gradient response as a mechanism through which same-class training data shape the retention of target learning and the reproduction of target images.

Problem

• Memorization
• Flow Matching
• Background Gradients
• Generative Models

Innovation

• Flow Matching
• Memorization
• Paired-Trajectory Framework
• Background Gradient Response
• Path-Integrated Curvature