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CAR-Flow: Condition-Aware Reparameterization Aligns Source and Target for Better Flow Matching
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Proposes CAR-Flow, a lightweight condition-dependent shift applied to the source and/or target distribution in flow matching, which shortens the learned probability path and improves SiT-XL/2 on ImageNet-256.
Problem
Standard conditional flow matching starts from a condition-agnostic Gaussian, forcing the velocity network to both transport mass and inject condition semantics, which slows convergence and can hurt sample quality.
Approach
Learn condition-dependent source and target maps restricted to additive shifts (no scale), which blocks the zero-cost collapse solutions of unrestricted reparameterization while shortening the transport path; the target map is approximately inverted at sampling time.
Key results
- On ImageNet-256 with cfg=1.5, joint CAR-Flow reduces SiT-XL/2 FID from 2.07 to 1.68 (IS 280.2 to 304.0) with under 0.6% extra parameters.
- Without cfg at 400K steps, joint CAR-Flow reaches FID 13.91 vs 17.28 for the SiT-XL/2 baseline.
- On CIFAR-10, source-only CAR-Flow reaches FID 7.5 vs 13.8 baseline.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add condition-aware shifts to both source and target | SiT-XL/2 · ImageNet-256, 7M steps, cfg=1.5 | FID: 2.07 -> 1.68 | Helped |
| Add condition-aware shifts to both source and target | SiT-XL/2 · ImageNet-256, 400K steps | FID: 17.28 -> 13.91 | Helped |
| Use a source shift only instead of shifting both source and target (ablation) | SiT-XL/2 CAR-Flow Joint · ImageNet-256, 400K steps | FID: 13.91 -> 15.15 | Hurt |
| Use a target shift only instead of shifting both source and target (ablation) | SiT-XL/2 CAR-Flow Joint · ImageNet-256, 400K steps | FID: 13.91 -> 14.44 | Hurt |
| Shift both source and target | Rectified flow · 1D synthetic data | Average trajectory length: 1.5355(24) -> 0.7121(11) | Helped |
| Use a source shift only instead of shifting both source and target (ablation) | Joint CAR-Flow · 1D synthetic data | Average trajectory length: 0.7121(11) -> 0.7432(19) | Hurt |
| Use a target shift only instead of shifting both source and target (ablation) | Joint CAR-Flow · 1D synthetic data | Average trajectory length: 0.7121(11) -> 0.7129(10) | Hurt |
| Add condition-aware shifts to both source and target | SiT-XL/2 · CIFAR-10, 400K steps | FID: 13.8 -> 10.6 | Helped |
| Use a source shift only instead of shifting both source and target (ablation) | Joint CAR-Flow · CIFAR-10, 400K steps | FID: 10.6 -> 7.5 | Helped |
| Use a target shift only instead of shifting both source and target (ablation) | Joint CAR-Flow · CIFAR-10, 400K steps | FID: 10.6 -> 11.1 | Hurt |
| Learn a condition-aware source shift rather than a single unconditional source shift (ablation) | Source-only CAR-Flow · 1D synthetic data | Wasserstein distance: 0.058 -> 0.041 | Helped |
| Increase the condition-network learning rate (ablation) | SiT-XL/2 CAR-Flow variants · ImageNet-256, 400K steps | FID: 12.77 at 2×10⁻² | Helped |
Surprising findings
- Unrestricted learned shift plus scale on source or target collapses to a single mode (mode collapse), with learned sigma shrinking toward zero.
- Target-only CAR-Flow reached the best FID (12.77) in the learning-rate sweep at 2e-2, not the joint variant.
Limitations
- Only shift-only maps are studied; more general (volume-preserving or expressive) reparameterizations are left to future work.
- Results are sensitive to the learning rate of the condition networks, with the optimum varying by variant and requiring tuning.
- Experiments on the synthetic data are limited to a 1D two-class mixture.
Experimental setup
Datasets: ImageNet CIFAR-10 synthetic 1D Gaussian mixture
Benchmarks: ImageNet 256x256 CIFAR-10 synthetic 1D Gaussian mixture
Metrics: FID IS sFID precision recall Wasserstein distance trajectory length
Baselines: SiT-XL/2 rectified flow SiT-XL/2 cfg=1.5
Builds on: SiT rectified flow REPA-E latent diffusion
Closest papers by meaning
- Coreset-Induced Conditional Velocity Flow Matching (NeurIPS 2026 · similarity 0.89)
- Reflected Flow Matching (ICML 2024 · similarity 0.89)
- Faster Inference of Flow-Based Generative Models via Improved Data-Noise Coupling (ICLR 2025 · similarity 0.89)
- On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticity (NeurIPS 2025 · similarity 0.88)
- Discrete Flow Matching (NeurIPS 2024 · similarity 0.88)
- Improving Flow Matching by Aligning Flow Divergence (ICML 2025 · similarity 0.88)
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