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Balanced Conic Rectified Flow
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Proposes balanced conic reflow, which alternates standard reflow on generated pairs with Slerp-perturbed reflow on real-image inversions to reduce drift in rectified flow and improve few-step generation with far fewer synthetic pairs.
Problem
Reflow in rectified flow requires many generated pairs and suffers from drift away from the real data distribution, error accumulation, and degraded full-step quality as reflow steps increase.
Approach
Supervise reflow with real pairs (reverse-inverted real images v^{-1}(X1), X1) expanded into a cone of neighbors via spherical linear interpolation (Slerp) with Gaussian noise, alternating with standard fake-pair reflow under a balanced schedule.
Key results
- On CIFAR-10, 2-rectified flow with the method reaches 1-step FID 5.98 (IS 8.79) versus 12.21 for the original 2-rectified flow, using 300K fake plus 60K real pairs instead of 4M fake pairs.
- On ImageNet 64x64 the method reports 1-step FID 5.662 for 4-rectified flow vs 6.580 for the original, and on the ImageNet table RK-45 FID 28.2 vs 31.2 for 2-rectified flow.
- RF++ with the method (600K fake + 50K real) achieves FID 3.84 vs 4.14 for RF++ at 1-step under Heun 2nd order sampling.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace original fake-pair reflow with balanced conic reflow using refreshed real pairs and Slerp | 2-rectified flow · CIFAR-10 1-step | FID: 12.21 -> 5.98 | Helped |
| add Slerp noise perturbation to conic real-pair supervision (ablation) | 2-rectified flow · CIFAR-10 1-step | FID: 6.60 -> 5.98 | Helped |
| periodically refresh real pairs instead of fixing the real pair once (ablation) | 2-rectified flow · CIFAR-10 1-step | FID: 6.69 -> 5.98 | Helped |
| use a cyclic increasing-then-decreasing Slerp schedule instead of a strictly decreasing schedule (ablation) | 2-rectified flow · CIFAR-10 1-step | FID: 6.70 -> 6.63 | Helped |
| replace Slerp with Lerp (ablation) | 2-rectified flow · CIFAR-10 1-step | FID: 6.63 -> 7.50 | Hurt |
| add Slerp supervision to real-only pair training (ablation) | 2-rectified flow · CIFAR-10 1-step | FID: 6.93 -> 6.71 | Helped |
| combine real pairs with fake pairs and Slerp instead of real-only Slerp supervision (ablation) | 2-rectified flow · CIFAR-10 1-step | FID: 6.71 -> 4.16 | Helped |
| combine real pairs with fake pairs and Slerp instead of real-only Slerp supervision (ablation) | 2-rectified flow · CIFAR-10 RK-step | FID: 4.47 -> 3.24 | Helped |
| add balanced conic reflow to RF++† | RF++† · CIFAR-10 1-step, 500K steps | FID: 4.14 -> 3.84 | Helped |
| add balanced conic reflow to RF++† | RF++† · CIFAR-10 2-step, 500K steps | FID: 3.16 -> 3.03 | Helped |
| replace original reflow with balanced conic reflow | 2-rectified flow · ImageNet 64×64 RK-45 | FID: 31.2 -> 28.2 | Helped |
| replace original reflow with balanced conic reflow | 4-rectified flow · CIFAR-10 1-step | FID: 6.580 -> 5.662 | Helped |
Surprising findings
- Reflow using only real pairs (no fake pairs) gives slight 1-step gains but progressively degrades full-step performance.
- Fine-tuning an existing official rectified flow checkpoint with 60K real pairs improves 1-step quality.
Limitations
- Choice of maximum Slerp noise magnitude zeta_max is dataset-dependent and selected heuristically without theoretical grounding.
- Real-only reflow degrades multi-step quality, so real pairs cannot replace synthetic pairs.
Experimental setup
Datasets: CIFAR-10 ImageNet 64x64 LSUN Bedroom two moons
Benchmarks: CIFAR-10 ImageNet 64x64 LSUN Bedroom
Metrics: FID IS precision recall curvature IVD reconstruction error perturbed reconstruction error
Baselines: 1-Rectified Flow 2-Rectified Flow 3-Rectified Flow RF++ SlimFlow Consistency Models EDM
Builds on: rectified flow reflow RF++ EDM PerFlow
Closest papers by meaning
- Improving the Training of Rectified Flows (NeurIPS 2024 · similarity 0.92)
- Rectified Diffusion: Straightness Is Not Your Need in Rectified Flow (ICLR 2025 · similarity 0.91)
- Simple ReFlow: Improved Techniques for Fast Flow Models (ICLR 2025 · similarity 0.90)
- ProReflow: Progressive Reflow with Decomposed Velocity (CVPR 2025 · similarity 0.88)
- Text-to-Image Rectified Flow as Plug-and-Play Priors (ICLR 2025 · similarity 0.88)
- Scaling Rectified Flow Transformers for High-Resolution Image Synthesis (ICML 2024 · similarity 0.87)
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