Likely Interpolants of Generative Models

Interpolation in generative models allows for controlled generation, model inspection, and more. Unfortunately, most generative models lack a principal notion of interpolants without restrictive assumptions on either the model or data dimension. In this paper, we develop a general interpolation scheme that targets likely transition paths compatible with different metrics and probability distributions. We consider interpolants analogous to a geodesic constrained to a suitable data distribution and derive a novel algorithm for computing these curves, which requires no additional training. Theoretically, we show that our method locally can be considered as a geodesic under a suitable Riemannian metric. We quantitatively show that our interpolation scheme traverses higher density regions than baselines across a range of models and datasets.