{"paper":{"title":"Coreset-Induced Conditional Velocity Flow Matching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A coreset-derived Gaussian mixture surrogate replaces isotropic noise in conditional velocity flow matching and equals the target-surrogate Wasserstein gap as transport cost.","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Jianxi Su, Xiao Wang, Zihua She","submitted_at":"2026-05-13T03:34:40Z","abstract_excerpt":"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 "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The explicit compression assumption that the coreset-derived Gaussian mixture surrogate sufficiently approximates the target velocity distribution so that the residual correction remains lightweight and the second-moment excess stays small.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"CCVFM replaces the inner noise source in hierarchical rectified flow matching with a data-informed Gaussian mixture surrogate from a Sinkhorn coreset, yielding a closed-form conditional velocity law and competitive few-step generation on MNIST, CIFAR-10, ImageNet-32, and CelebA-HQ.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A coreset-derived Gaussian mixture surrogate replaces isotropic noise in conditional velocity flow matching and equals the target-surrogate Wasserstein gap as transport cost.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1e0dfafb39063b24f95df5ef567e219b1da279b851558731a50d56579037b6fe"},"source":{"id":"2605.12951","kind":"arxiv","version":1},"verdict":{"id":"ed2ac339-632b-452d-bbfc-92b0c32cd570","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:52:26.806431Z","strongest_claim":"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.","one_line_summary":"CCVFM replaces the inner noise source in hierarchical rectified flow matching with a data-informed Gaussian mixture surrogate from a Sinkhorn coreset, yielding a closed-form conditional velocity law and competitive few-step generation on MNIST, CIFAR-10, ImageNet-32, and CelebA-HQ.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The explicit compression assumption that the coreset-derived Gaussian mixture surrogate sufficiently approximates the target velocity distribution so that the residual correction remains lightweight and the second-moment excess stays small.","pith_extraction_headline":"A coreset-derived Gaussian mixture surrogate replaces isotropic noise in conditional velocity flow matching and equals the target-surrogate Wasserstein gap as transport cost."},"references":{"count":33,"sample":[{"doi":"","year":2025,"title":"Stochastic interpolants: A unifying framework for flows and diffusions.Journal of Machine Learning Research, 26(209):1–80, 2025","work_id":"de67e3e2-0833-42ff-9811-8e8aba9ce4c7","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"Reconstructing training data with informed adversaries","work_id":"7114b5ec-863a-4a52-a373-1fd855ec2bbc","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"Pros and cons of GAN evaluation measures","work_id":"6b163ab9-b909-4947-9e26-b1c169457ee6","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Extracting training data from diffusion models","work_id":"06d16fb5-0847-44cf-9994-315dbbc65150","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"A downsampled variant of imagenet as an alternative to the CIFAR datasets","work_id":"b28da76e-30a0-4103-a956-55ca47f3e243","ref_index":5,"cited_arxiv_id":"1707.08819","is_internal_anchor":true}],"resolved_work":33,"snapshot_sha256":"5a7d15e1971cb900ec2d686a8ed63320674634ab65f119c9a063999ed599a51c","internal_anchors":2},"formal_canon":{"evidence_count":2,"snapshot_sha256":"594e919564e51f6fa5e21db8893ec24572fec0003b5ac24bcff2cf2ba60f48f5"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}