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Faster Inference of Flow-Based Generative Models via Improved Data-Noise Coupling
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Proposes LOOM-CFM, which preserves and iteratively refines minibatch OT noise-data assignments across minibatches and training time, with multiple noise caches per data point, to straighten CFM sampling trajectories.
Problem
Minibatch OT couplings used in conditional flow matching become less effective as datasets grow, because assignments are optimized only within individual minibatches, leaving sampling trajectories curved and requiring many NFEs.
Approach
Cache the local Hungarian assignments computed in each minibatch and reuse them in future iterations so that the global data-noise permutation is improved over training, and store several noise samples per data point (noise caches) to avoid overfitting to a fixed pairing.
Key results
- On CIFAR10 with 4 caches and midpoint solver at 12 NFE, FID 4.60 vs. OT-CFM 7.77 (about 41% reduction).
- On ImageNet-64 at 12 NFE, FID 8.49 vs. MFM w/ BatchOT 18.27 (about 54% reduction).
- On FFHQ-256 latent training, FID 6.76 at 4 NFE and 4.77 with dopri5 at 77 NFE, compared with LDM's 4.98 at 50 NFE.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use LOOM-CFM coupling assignments instead of minibatch OT | CFM · CIFAR10, 4 NFE | FID: 15.95 -> 11.60 | Helped |
| use LOOM-CFM coupling assignments instead of minibatch OT | CFM · CIFAR10, 8 NFE | FID: 9.73 -> 5.38 | Helped |
| use LOOM-CFM coupling assignments instead of minibatch OT | CFM · ImageNet-32, 12 NFE | FID: 4.11 -> 3.89 | Helped |
| use LOOM-CFM coupling assignments instead of minibatch OT | CFM · ImageNet-64, 12 NFE | FID: 11.58 -> 8.49 | Helped |
| add one reflow stage to LOOM-CFM | LOOM-CFM, CIFAR10 · CIFAR10, 1 NFE | FID | Helped |
| wait for matching convergence before starting vector-field training (ablation) | LOOM-CFM, CIFAR10 · CIFAR10 | FID | Hurt |
| omit saving and reusing local reassignments (ablation) | LOOM-CFM, CIFAR10 · CIFAR10, few NFE | FID | Hurt |
| use a fixed initial noise-data assignment without reassignments (ablation) | LOOM-CFM, CIFAR10 · CIFAR10 | FID | Hurt |
| increase noise caches from 2 to 4 (ablation) | LOOM-CFM, CIFAR10 · CIFAR10, 8 NFE | FID: 9.93 -> 5.38 | Helped |
| increase noise caches from 3 to 4 (ablation) | LOOM-CFM, CIFAR10 · CIFAR10, 8 NFE | FID: 6.40 -> 5.38 | Helped |
| increase batch size from 32 to 128 (ablation) | LOOM-CFM, 4 caches · CIFAR10, 8 NFE | FID: 9.56 -> 5.38 | Helped |
| increase batch size from 64 to 128 (ablation) | LOOM-CFM, 4 caches · CIFAR10, 8 NFE | FID: 8.85 -> 5.38 | Helped |
Surprising findings
- Training with a fixed noise source and no reassignments gives better FID at 4 and 8 NFE than OT-CFM, though worse than LOOM-CFM overall.
- A single reflow stage initialized by LOOM-CFM outperforms 2- and 3-Rectified Flow on CIFAR10.
Limitations
- Not directly compatible with conditional generation; naive label conditioning may introduce sampling bias.
- Converges only to a stationary sub-optimal matching, with no global optimality guarantee.
- Convergence slows as dataset size (number of noise caches) grows.
Experimental setup
Datasets: CIFAR10 ImageNet-32 ImageNet-64 FFHQ-256
Benchmarks: CIFAR10 ImageNet-32 ImageNet-64 FFHQ-256
Metrics: FID NFE
Baselines: OT-CFM MFM w/ BatchOT MFM w/ Stable NFDM-OT Rectified Flow DDPM FM w/ OT I-CFM DPM Solver LDM Latent Flow Matching
Builds on: Conditional Flow Matching OT-CFM BatchOT Rectified Flow ADM
Closest papers by meaning
- Improving Flow Matching by Aligning Flow Divergence (ICML 2025 · similarity 0.91)
- Optimal Flow Matching: Learning Straight Trajectories in Just One Step (NeurIPS 2024 · similarity 0.89)
- Blockwise Flow Matching: Improving Flow Matching Models For Efficient High-Quality Generation (NeurIPS 2025 · similarity 0.89)
- CAR-Flow: Condition-Aware Reparameterization Aligns Source and Target for Better Flow Matching (NeurIPS 2025 · similarity 0.89)
- Discrete Flow Matching (NeurIPS 2024 · similarity 0.89)
- Diff2Flow: Training Flow Matching Models via Diffusion Model Alignment (CVPR 2025 · similarity 0.89)
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