Learning Straight Flows by Learning Curved Interpolants
This work addresses a bottleneck in generative modeling for researchers and practitioners, offering an incremental improvement over existing flow matching methods.
The paper tackles the problem of slow inference in flow matching models by proposing to learn flexible interpolants to achieve straight vector fields, resulting in faster generation.
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.