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Taming Rectified Flow for Inversion and Editing
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Proposes RF-Solver, a training-free second-order Taylor-expansion sampler that reduces ODE-solving error for rectified-flow models (FLUX, OpenSora) to improve inversion and reconstruction, and RF-Edit, a self-attention value-sharing editing framework built on it for image and video editing.
Problem
Rectified-flow diffusion transformers such as FLUX and OpenSora show poor inversion/reconstruction accuracy because the Euler sampler accumulates ODE-solving error, which limits downstream image and video editing.
Approach
Derive the exact variation-of-constants solution of the rectified flow ODE and approximate the nonlinear integral with a Taylor expansion; estimate the first derivative of the velocity field with one extra forward pass, and share attention value features from inversion into denoising for editing.
Key results
- On image inversion with FLUX, RF-Solver reduces MSE from 0.0268 (vanilla RF) to 0.0092 and raises PSNR from 28.28 to 29.89.
- On text-to-image sampling with FLUX at equal NFE, FID improves from 25.33 (RF) to 23.98 and CLIP score from 31.01 to 31.09.
- For image editing, RF-Edit reaches CLIP score 33.66 versus 33.02 for RF-Inversion, with LPIPS 0.149 (PnP has lowest LPIPS at 0.080 but lowest CLIP score).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use second-order Taylor expansion instead of vanilla rectified flow (ablation) | RF-Solver · Image sampling | FID: 25.33 -> 23.98 | Helped |
| Use second-order Taylor expansion instead of vanilla rectified flow (ablation) | RF-Solver · Image inversion | MSE: 0.0268 -> 0.0092 | Helped |
| Use second-order Taylor expansion instead of vanilla rectified flow (ablation) | RF-Solver · Image editing | CLIP Score: 32.97 -> 33.66 | Helped |
| Use third-order rather than second-order Taylor expansion (ablation) | RF-Solver · Image sampling | FID: 23.98 -> 23.94 | Helped |
| Use third-order rather than second-order Taylor expansion (ablation) | RF-Solver · Image sampling | CLIP Score: 31.09 -> 31.09 | No clear effect |
| Use third-order rather than second-order Taylor expansion (ablation) | RF-Solver · Image inversion | MSE: 0.0092 -> 0.0131 | Hurt |
| Use third-order rather than second-order Taylor expansion (ablation) | RF-Solver · Image inversion | LPIPS: 0.4239 -> 0.4817 | Hurt |
| Use third-order rather than second-order Taylor expansion (ablation) | RF-Solver · Image editing | CLIP Score: 33.66 -> 33.18 | Hurt |
| Share inversion self-attention value features during editing (ablation) | RF-Edit · Image editing | CLIP Score | Helped |
| Increase the number of feature-sharing steps excessively (ablation) | RF-Edit · Image editing | editing fidelity | Hurt |
Surprising findings
- Higher-order (third-order) Taylor expansion did not improve over second order under a fixed NFE budget, since fewer timesteps are then available.
- PnP achieves the lowest LPIPS in image editing yet the lowest CLIP score, because it fails on shape-changing edits and stays close to the source.
Limitations
- Derivative estimation requires an extra network forward pass per timestep, doubling cost at equal step count.
- Higher-order expansions require more NFE per step and become impractical under a fixed budget.
- Video evaluation uses about 40 videos and image editing uses about 300 images, with mostly self-collected data and hyperparameters tuned per case.
Experimental setup
Datasets: MS-COCO validation DIV2K social media videos (TikTok and public sources, ~40 videos)
Benchmarks: MS-COCO validation (FID, CLIP score) inversion reconstruction image and video sets image editing set (over 300 images) VBench video editing metrics
Metrics: FID CLIP Score MSE LPIPS SSIM PSNR Subject Consistency Motion Smoothness Aesthetic Quality Imaging Quality
Baselines: RF (vanilla Euler sampler) RF-Heun DPM-Solver++ P2P DiffEdit SDEdit PnP Pix2Pix RF-Inversion FateZero FLATTEN COVE
Builds on: rectified flow DDIM inversion Heun sampler DPM-Solver++ RF-Inversion
Closest papers by meaning
- Semantic Image Inversion and Editing using Rectified Stochastic Differential Equations (ICLR 2025 · similarity 0.92)
- FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing (ICML 2025 · similarity 0.90)
- Unveil Inversion and Invariance in Flow Transformer for Versatile Image Editing (CVPR 2025 · similarity 0.89)
- Text-to-Image Rectified Flow as Plug-and-Play Priors (ICLR 2025 · similarity 0.88)
- High-Fidelity Diffusion-Based Image Editing (AAAI 2024 · similarity 0.88)
- Lightning-Fast Image Inversion and Editing for Text-to-Image Diffusion Models (ICLR 2025 · similarity 0.88)
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