Localizing Conditional Transport in Triangular Flows

Conditional flow-based generative models amortize sampling across a family of distributions with a single velocity field, but a globally fixed interpolation schedule can fail to accommodate heterogeneous geometry across the conditioning space. We study whether adapting the interpolation schedule to the conditioning variable, leading to localized interpolants, improves the learnability of triangular flow models. We construct geometry-dependent schedules that homogenize the induced velocity across conditionals, not merely reduce its stiffness at each one, so that a single finite-capacity network approximates the entire family more accurately.