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Rectified Diffusion: Straightness Is Not Your Need in Rectified Flow
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Argues that rectified flow's benefit comes from retraining on pre-generated noise-sample pairs from a pretrained diffusion model, not from flow-matching or v-prediction; proposes Rectified Diffusion, which targets a first-order ODE path for general diffusion models and applies it to Stable Diffusion v1-5 and SDXL.
Problem
Rectified flow speeds up diffusion sampling by straightening ODE paths, but it requires flow-matching form and v-prediction, and its expensive training (e.g., InstaFlow) limits practicality for pretrained DDPM-style diffusion models.
Approach
Rectification's essential ingredient is retraining on deterministic noise-sample pairs generated by a pretrained diffusion model; the real training target is a first-order ODE path (not straightness), which generalizes to any diffusion form, so the pretrained model's formulation can be kept unchanged. Consistency distillation is then applied on top of the first-order path, and a phased variant enf
Key results
- Rectified Diffusion 1-step FID 27.26 vs Rectified Flow 1-step FID 47.91 on COCO-2017 (512px, SDv1-5)
- Rectified Diffusion trained with about 20 A800 GPU days vs InstaFlow's 75.2 A100 GPU days; consistency distillation used 4.6 A800 GPU days vs InstaFlow distillation 110 A100 GPU days
- Rectified Diffusion-XL (Phased) 4-step FID 19.71 vs PeRFlow-XL 20.99 on COCO-2014 10k
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace flow-matching rectification with paired noise-image retraining in the original diffusion configuration | Stable Diffusion v1-5 · COCO-2014 validation, 1 step | FID: 36.68 -> 16.88 | Helped |
| Replace flow-matching rectification with paired noise-image retraining in the original diffusion configuration | Stable Diffusion v1-5 · COCO-2014 validation, 2 steps | FID: 20.01 -> 12.57 | Helped |
| Use consistency distillation instead of the InstaFlow distillation approach | Rectified Diffusion · COCO-2014 validation, 1 step | FID: 13.67 -> 12.54 | Helped |
| Use consistency distillation instead of the InstaFlow distillation approach | Rectified Diffusion · COCO-2014 validation, 2 steps | FID: 62.81 -> 11.41 | Helped |
| Segment the ODE path into phases and enforce first-order property within each phase | Stable Diffusion v1-5 · COCO-2014 validation, 1 step | FID: 18.59 -> 10.21 | Helped |
| Segment the ODE path and enforce first-order property within each phase | Stable Diffusion XL · COCO-2014 validation, 4 steps, 1024 resolution | FID: 20.99 -> 19.71 | Helped |
| Segment the ODE path and enforce first-order property within each phase | Stable Diffusion v1-5 · COCO-2017 validation, 4 steps | FID: 22.97 -> 20.64 | Helped |
Surprising findings
- Straightness of the ODE path is not essential; a first-order ODE path can be inherently curved for DDPM and Sub-VP forms, and v-prediction and flow-matching are unnecessary for rectification.
Limitations
- Low-step performance still lags behind state-of-the-art distillation and GAN-based methods, requiring additional distillation.
- Ideal first-order path is not perfectly achieved due to optimization, model capacity, and ODE path intersections.
- Phased variant increases the minimum number of generation steps to the number of segments.
Experimental setup
Datasets: COCO-2014 COCO-2017 Pick-a-pic randomly sampled prompts (1.6M) with SD v1-5 generated images
Benchmarks: COCO-2017 validation COCO-2014 30k (Karpathy split) COCO-2014 10k (SDXL evaluation) Pick-a-pic validation
Metrics: FID CLIP score win rate Laion-Aesthetic Predictor PickScore HPSv2 ImageReward
Baselines: Rectified Flow InstaFlow Rectified Flow (Distill) PeRFlow PeRFlow-XL SDXL-Turbo SDXL-Lightning DMDv2 LCM Phased Consistency Model UFOGen DMD
Builds on: rectified flow InstaFlow PeRFlow consistency distillation DPM-Solver
Closest papers by meaning
- Improving the Training of Rectified Flows (NeurIPS 2024 · similarity 0.94)
- ProReflow: Progressive Reflow with Decomposed Velocity (CVPR 2025 · similarity 0.92)
- Text-to-Image Rectified Flow as Plug-and-Play Priors (ICLR 2025 · similarity 0.92)
- Balanced Conic Rectified Flow (NeurIPS 2025 · similarity 0.91)
- Simple ReFlow: Improved Techniques for Fast Flow Models (ICLR 2025 · similarity 0.91)
- Diff2Flow: Training Flow Matching Models via Diffusion Model Alignment (CVPR 2025 · similarity 0.90)
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