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arXiv · 2602.02793

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

Reza Rezvan·Gustav Gille·Moritz Schauer·Richard Torkar
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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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Reza Rezvan, Gustav Gille, Moritz Schauer, Richard Torkar. 2026-02-02. Causality--Δ: Jacobian-Based Dependency Analysis in Flow Matching Models. https://arxiv.org/abs/2602.02793

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