Causality--Δ: Jacobian-Based Dependency Analysis in Flow Matching Models
This work provides a method for understanding feature dependencies in generative models, which is incremental as it applies existing Jacobian techniques to flow matching.
The paper tackled the problem of analyzing dependency structures in flow matching models by using Jacobian-vector products to study how latent perturbations propagate, and showed that conditioning on small classifier-Jacobian norms reduces correlations in image datasets like MNIST and CelebA.
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.