Variational Rectified Flow Matching

• URL: http://arxiv.org/abs/2502.09616v1
• Date: Thu, 13 Feb 2025 18:59:15 GMT
• Title: Variational Rectified Flow Matching
• Authors: Pengsheng Guo, Alexander G. Schwing,
• Abstract summary: Variational Rectified Flow Matching enhances classic rectified flow matching by modeling multi-modal velocity vector-fields. We show on synthetic data that variational rectified flow matching leads to compelling results.
• Score: 100.63726791602049
• License:
• 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. In contrast, variational rectified flow matching learns and samples from multi-modal flow directions. We show on synthetic data, MNIST, CIFAR-10, and ImageNet that variational rectified flow matching leads to compelling results.

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