Learning Straight Flows by Learning Curved Interpolants
Shiv Shankar, Tomas Geffner
TL;DR
This work addresses slow sampling in flow-matching generative models by targeting curved velocity fields that transport samples from $p_0$ to $p_1$. The authors introduce a bi-level framework that learns straight flows by tuning flexible interpolants $\phi$ in conditional flow matching and derive an analytic form for the target field $v^*$ to avoid inner differentiable optimization. By parameterizing interpolants with invertible networks (e.g., $\text{GLOW}$), the approach enables scalable, end-to-end, simulation-free training and exact Jacobian computations, facilitating efficient generation. Empirically, the method improves generation quality at low function evaluations (NFE) on CIFAR-10, ImageNet-32x32, and CelebA-HQ, outperforming several baselines and offering practical speedups for high-dimensional generation tasks.
Abstract
Flow matching models typically use linear interpolants to define the forward/noise addition process. This, together with the independent coupling between noise and target distributions, yields a vector field which is often non-straight. Such curved fields lead to a slow inference/generation process. In this work, we propose to learn flexible (potentially curved) interpolants in order to learn straight vector fields to enable faster generation. We formulate this via a multi-level optimization problem and propose an efficient approximate procedure to solve it. Our framework provides an end-to-end and simulation-free optimization procedure, which can be leveraged to learn straight line generative trajectories.