Learning Straight Flows by Learning Curved Interpolants

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.

@article{shankar2025_2503.20719,
  title={ Learning Straight Flows by Learning Curved Interpolants },
  author={ Shiv Shankar and Tomas Geffner },
  journal={arXiv preprint arXiv:2503.20719},
  year={ 2025 }
}