Causality--Δ: Jacobian-Based Dependency Analysis in Flow Matching Models

• URL: http://arxiv.org/abs/2602.02793v1
• Date: Mon, 02 Feb 2026 20:52:52 GMT
• Title: Causality--Δ: Jacobian-Based Dependency Analysis in Flow Matching Models
• Authors: Reza Rezvan, Gustav Gille, Moritz Schauer, Richard Torkar,
• Abstract summary: Flow matching learns a velocity field that transports a base distribution to data.<n>We study how small latent perturbations propagate through these flows and show that Jacobian-vector products (JVPs) provide a practical lens on dependency structure in the generated features.
• Score: 2.7182326722409385
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Flow matching learns a velocity field that transports a base distribution to data. We study how small latent perturbations propagate through these flows and show that Jacobian-vector products (JVPs) provide a practical lens on dependency structure in the generated features. We derive closed-form expressions for the optimal drift and its Jacobian in Gaussian and mixture-of-Gaussian settings, revealing that even globally nonlinear flows admit local affine structure. In low-dimensional synthetic benchmarks, numerical JVPs recover the analytical Jacobians. In image domains, composing the flow with an attribute classifier yields an attribute-level JVP estimator that recovers empirical correlations on MNIST and CelebA. Conditioning on small classifier-Jacobian norms reduces correlations in a way consistent with a hypothesized common-cause structure, while we emphasize that this conditioning is not a formal do intervention.

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