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SCoT: Unifying Consistency Models and Rectified Flows via Straight-Consistent Trajectories
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Proposes SCoT, a trajectory projection model that jointly enforces constant velocity (straightness, via gradient of the mapping w.r.t. end time s) and trajectory consistency, distilling pre-trained diffusion teachers for 1- and 2-step sampling on CIFAR-10 and ImageNet 64.
Problem
Distilled diffusion samplers either need many steps (consistency models/CTM with curved trajectories) or rely on numerical ODE solves whose approximation errors degrade quality (rectified flow/reflow).
Approach
Learn a projection G(x_t,t,s) whose partial derivative in s is constrained to match the teacher's pair displacement (x0_hat - x1), giving straight trajectories without ODE solving, while a soft-consistency loss enforces that points on the same teacher trajectory map to the same output.
Key results
- On CIFAR-10, SCoT reaches FID 2.30 at 2 NFE, beating CD (2.93) and CT (5.83); CTM gets 1.87 at 1 NFE but uses a GAN loss that SCoT omits.
- On ImageNet 64, SCoT reaches FID 2.60 at 2 NFE (IS 68.2) and 4.80 at 1 NFE, versus CD 6.20 and PD 15.39 at 2 NFE.
- Ablation on ImageNet shows FID dropping from 14.7 to 4.8 at NFE=1 when the velocity regularization is added (per their velocity-guarantee table).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add trajectory consistency loss (ablation) | SCoT · ImageNet, NFE=1, 20k iterations | FID: 15.7 -> 5.6 | Helped |
| add trajectory consistency loss (ablation) | SCoT · ImageNet, NFE=2, 20k iterations | FID: 16.4 to 3.9 | Helped |
| add velocity guarantee loss (ablation) | SCoT · ImageNet, NFE=1, 20k iterations | FID: 14.7 to 4.8 | Helped |
| add velocity guarantee loss (ablation) | SCoT · ImageNet, NFE=2, 20k iterations | FID: 15.2 to 2.6 | Helped |
| use adaptive velocity-loss weighting instead of normalization (ablation) | SCoT · ImageNet, 20k iterations | FID: 3.6 -> 6.2 | Hurt |
| remove adaptive velocity-loss scaling (ablation) | SCoT · ImageNet, 20k iterations | FID: 3.6 -> 7.0 | Hurt |
Surprising findings
- Without the GAN loss, SCoT trails CTM at 1 NFE on ImageNet (4.80 vs 1.92), and the paper attributes CTM's advantage to GAN supervision.
- Velocity (second-order autograd) loss proved unstable, requiring loss normalization/clipping to weight in [0.01, 10].
Limitations
- Trained only by distillation from pre-trained teachers; training from scratch was not explored due to resource constraints.
- Lacks GAN loss, so it underperforms CTM* (GAN-augmented) at 1 NFE; GAN loss was unstable in their setup.
- Evaluated only on low-resolution data (CIFAR-10 32x32, ImageNet 64x64).
Experimental setup
Datasets: CIFAR-10 ImageNet 64x64
Benchmarks: CIFAR-10 ImageNet 64x64
Metrics: FID sFID Inception Score Precision Recall FLOPs MACs parameters training throughput
Baselines: Reflow InstaFlow SlimFlow CTM Consistency Distillation (CD) Consistency Training (CT) Progressive Distillation (PD) Shortcut model DDIM DPM-solver 3-DEIS EDM
Builds on: Consistency Trajectory Model (CTM) Reflow / rectified flow Consistency Models Shortcut models EDM
Closest papers by meaning
- Improving the Training of Rectified Flows (NeurIPS 2024 · similarity 0.90)
- Accelerating Rectified Flow Models via Trajectory-Aware Caching (NeurIPS 2026 · similarity 0.89)
- How to build a consistency model: Learning flow maps via self-distillation (NeurIPS 2025 · similarity 0.89)
- Elucidating Flow Matching ODE Dynamics via Data Geometry and Denoisers (ICML 2025 · similarity 0.88)
- Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion (ICLR 2024 · similarity 0.88)
- Test-time Scaling of Diffusions with Flow Maps (NeurIPS 2026 · similarity 0.88)
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