Research map / Probabilistic and scientific modeling / Variational and generative sampling
Coreset-Induced Conditional Velocity Flow Matching
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes CCVFM, which replaces the isotropic Gaussian source in hierarchical rectified flow (HRF2) with a closed-form coreset-GMM surrogate built via entropic Sinkhorn, then trains a correction flow from that surrogate source for few-step image generation.
Problem
Hierarchical velocity-space flow matching must transport isotropic Gaussian noise to a multimodal target velocity law from scratch, making low-NFE generation hard.
Approach
Use an entropic-Sinkhorn coreset lifted to a GMM as a data-informed source; its induced conditional velocity law is closed-form GMM, so a correction flow only needs to learn the surrogate-to-target residual, with Sinkhorn-anchored coupling giving exact marginal preservation.
Key results
- MNIST FID50k 0.75 at 51 NFE (vs HRF2 2.574 at 500 NFE).
- ImageNet-32 FID50k 8.76 at 51 NFE vs HRF2 9.02 at 51 NFE; 38% better than HRF2 at 11 NFE.
- CelebA-HQ 256 FID28k 4.17 at 51 NFE with DiT-L in DC-AE latent space; CIFAR-10 FID50k 6.35 at 51 NFE, behind EDM 1.97 at 35 NFE.
Surprising findings
- On CIFAR-10 the method trails EDM (1.97 at 35 NFE), and it does not beat HRF2 at 51 NFE on ImageNet-32 by a meaningful margin.
Limitations
- Stage-I compression rate is assumed rather than proven for the entropic-Sinkhorn/GMM procedure.
- High-dimensional constants are pessimistic; NFE scaling relies on residual-field flattening assumptions.
- Single-seed point estimates; EDM retains a lead on CIFAR-10 at matched NFE.
Experimental setup
Datasets: MNIST CIFAR-10 ImageNet-32 CelebA-HQ 256
Benchmarks: MNIST CIFAR-10 ImageNet-32 CelebA-HQ 256
Metrics: FID precision/recall 1-NN KS and Wasserstein-1 memorization test
Baselines: HRF2 Rectified Flow DDPM Flow Matching EDM CM LSGM ADM LDM-4
Builds on: hierarchical rectified flow rectified flow conditional flow matching Tipping-Bishop PPCA
Closest papers by meaning
- CAR-Flow: Condition-Aware Reparameterization Aligns Source and Target for Better Flow Matching (NeurIPS 2025 · similarity 0.89)
- Reflected Flow Matching (ICML 2024 · similarity 0.89)
- A Theory on Flow Matching with Neural Networks (NeurIPS 2026 · similarity 0.89)
- Blockwise Flow Matching: Improving Flow Matching Models For Efficient High-Quality Generation (NeurIPS 2025 · similarity 0.88)
- Faster Inference of Flow-Based Generative Models via Improved Data-Noise Coupling (ICLR 2025 · similarity 0.88)
- Structured Coupling for Flow Matching (NeurIPS 2026 · similarity 0.88)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.