Coreset-Induced Conditional Velocity Flow Matching

2026-05-14 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Emerging Technologies & Innovation · Depth: Expert, long

Summary

Coreset-Induced Conditional Velocity Flow Matching (CCVFM) is a generative model that enhances hierarchical rectified flow (HRF2) by replacing its isotropic Gaussian noise source with a data-informed, closed-form surrogate distribution. HRF2 models the full conditional velocity law but struggles with multimodal target velocity distributions, requiring high Numbers of Function Evaluations (NFE). CCVFM addresses this by compressing the target data into weighted atoms using an entropic Sinkhorn coreset, which is then lifted to a Gaussian Mixture Model (GMM). This GMM provides a closed-form conditional velocity law that can be sampled without a learned neural sampler. A lightweight correction flow then refines the residual between this surrogate and the target, rather than learning the entire noise-to-data map. The method achieves competitive few-step generation on datasets like MNIST (FID 0.75), CIFAR-10 (FID 6.35), ImageNet-32 (FID 8.76), and CelebA-HQ (FID 4.17) at 51 NFE.

Key takeaway

Research scientists developing generative models should consider CCVFM's approach to improve few-step generation efficiency. By adopting a data-informed coreset surrogate, you can significantly reduce the NFE required compared to traditional noise-to-data mapping, especially when dealing with multimodal target distributions. This method offers a more direct and computationally less intensive path to high-fidelity sample generation, potentially accelerating model development and deployment.

Key insights

CCVFM improves generative flow matching by using a data-informed coreset surrogate instead of isotropic noise.

Principles

• Replace isotropic noise sources with data-informed surrogates.
• Model full conditional velocity laws for multimodal targets.
• Compress target data into weighted atoms for efficient representation.

Method

CCVFM involves three stages: building a coreset-GMM surrogate, deriving its closed-form conditional velocity law, and training a correction flow to refine the surrogate-to-target residual.

In practice

• Use entropic Sinkhorn coresets for data compression.
• Employ GMMs to represent conditional velocity laws.
• Train correction networks on surrogate-to-target residuals.

Topics

• Coreset-Induced Conditional Velocity Flow Matching
• Hierarchical Rectified Flow
• Flow Matching
• Entropic Sinkhorn Coreset
• Gaussian Mixture Models

Best for: Research Scientist, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.