Coreset-Induced Conditional Velocity Flow Matching

• URL: http://arxiv.org/abs/2605.12951v1
• Date: Wed, 13 May 2026 03:34:40 GMT
• Title: Coreset-Induced Conditional Velocity Flow Matching
• Abstract summary: We propose a generative model that augments hierarchical rectified flow with a data-informed source distribution.<n>Key observation is that this inner source can be replaced by a closed-form surrogate built from a coreset of the target.<n>A lightweight correction flow, trained from this exact surrogate source, then refines the remaining surrogate-to-target residual.
• Score: 4.297295761793895
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose Coreset-Induced Conditional Velocity Flow Matching (CCVFM), a generative model that augments hierarchical rectified flow with a data-informed source distribution. Hierarchical flow matching models the full conditional velocity law in velocity space, but its inner flow is asked to transport isotropic Gaussian noise to a multimodal target velocity distribution from scratch. Our key observation is that this inner source can be replaced by a closed-form surrogate built from a coreset of the target. CCVFM first compresses the target into weighted atoms using an entropic Sinkhorn coreset and lifts them to a Gaussian mixture. The induced conditional velocity law is then a closed-form Gaussian mixture that can be sampled without a learned neural sampler. A lightweight correction flow, trained from this exact surrogate source, then refines the remaining surrogate-to-target residual rather than learning an entire noise-to-data map. We prove that the surrogate transport cost equals the target--surrogate Wasserstein gap under an explicit compression assumption, whereas the noise-source analogue has a dimension-scale lower bound. We further characterize the conditional second moment of the direct surrogate-source training target and show that its source-dependent excess is small when the surrogate conditional law is close to the true conditional velocity law in mean and covariance. Empirically, on MNIST, CIFAR-10, ImageNet-32, and CelebA-HQ, the proposed method reaches competitive few-step generation under matched architectures.

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