Learning Straight Flows by Learning Curved Interpolants

Shiv Shankar; Tomas Geffner

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arXiv · 2503.20719

Learning Straight Flows by Learning Curved Interpolants

Shiv Shankar·Tomas Geffner

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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.

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Shiv Shankar, Tomas Geffner. 2025-03-26. Learning Straight Flows by Learning Curved Interpolants. https://arxiv.org/abs/2503.20719

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