Variational Rectified Flow Matching

Pengsheng Guo, Alex Schwing

Keywords: Flow Matching, Diffusion Model, Generative Model

Abstract: We study Variational Rectified Flow Matching, a framework that enhances classic rectified flow matching by modeling multi-modal velocity vector-fields. At inference time, classic rectified flow matching 'moves' samples from a source distribution to the target distribution by solving an ordinary differential equation via integration along a velocity vector-field. At training time, the velocity vector-field is learnt by linearly interpolating between coupled samples one drawn from the source and one drawn from the target distribution randomly. This leads to ''ground-truth'' velocity vector-fields that point in different directions at the same location, i.e., the velocity vector-fields are multi-modal/ambiguous. However, since training uses a standard mean-squared-error loss, the learnt velocity vector-field averages ''ground-truth'' directions and isn't multi-modal. Further, averaging leads to integration paths that are more curved while making it harder to fit the target distribution. In contrast, the studied variational rectified flow matching is able to capture the ambiguity in flow directions. We show on synthetic data, MNIST, and CIFAR-10 that the proposed variational rectified flow matching leads to compelling results with fewer integration steps.

Primary Area: generative models

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Submission Number: 1994