JIVE: Jacobian-Informed Volume Expansion for Diverse Generative Sampling

2026-09-27

AI Summary

This study addresses the challenges of mode collapse and insufficient sample diversity in generative models by proposing a training-free framework. Methodologically, it computes perturbation directions via matrix-free iterative algorithms grounded in numerical linear algebra, injecting velocity perturbations aligned with the principal singular subspace of the endpoint Jacobian. By leveraging local geometric structures, this approach explicitly maximizes endpoint diversity while preserving generation quality. Both theoretical analysis and empirical results demonstrate that the proposed method effectively enhances diversity without requiring additional training, yielding significant improvements in pixel-level and feature-level sample diversity for few-step and one-step generation tasks.

Abstract

Generative models often suffer from mode collapse and limited sample diversity. While prior works attempt to mitigate this by jointly generating a batch of samples and repelling their trajectories, these heuristics do not explicitly maximize the diversity of the resulting endpoints. We introduce JIVE, a training-free framework that enhances generative diversity by injecting velocity perturbations aligned with the leading right singular subspace of the generator's endpoint Jacobian. By leveraging this local geometric structure, JIVE provably maximizes endpoint diversity while preserving sample quality. To maintain practical efficiency, we compute these perturbation directions via matrix-free iterations rooted in classical numerical linear algebra, requiring only a small computational overhead. Across different benchmarks, JIVE boosts both pixel and feature-level diversity in few-step and one-step generation.

Problem

• Generative models
• Mode collapse
• Sample diversity
• Endpoint diversity

Innovation

• Training-free framework
• Endpoint Jacobian
• Singular subspace perturbation
• Matrix-free iterations
• Generative diversity