Overview
Flow matching learns a velocity field that transports a simple base distribution into a data distribution. Causality-Δ studies how small latent perturbations propagate through that learned flow, using Jacobian-vector products as a practical lens on dependency structure in generated features.
The paper connects analytical calculations in Gaussian and mixture-of-Gaussian settings with numerical experiments in low-dimensional data and image domains. The central point is local. Even when the global flow is nonlinear, its Jacobian can expose how changes in one latent direction influence generated attributes nearby.
Why It Matters
Generative models are often evaluated by sample quality, but scientific use also requires understanding what structure they have learned. Jacobian-based analysis gives a way to interrogate the learned dynamics without treating the model as a black box. The work is careful about the distinction between observational dependency and formal intervention. The method provides evidence about local dependencies, not a general do-calculus oracle.
My Role
This project was my first sustained research work on generative models as dynamical systems. It sharpened my interest in the mathematical structure of modern ML models. I care about what the model represents locally, how uncertainty propagates, and when the learned geometry can be connected to causal hypotheses.