Root-Selecting Fixed-Point Inversion for Rectified Flows via Trajectory Straightness

Rectified-flow-based diffusion transformers, particularly FLUX, have demonstrated outstanding performance in high-quality image generation. However, achieving fast and accurate inversion--transforming images back to latent noise for faithful reconstruction and editing--remains a challenging bottleneck due to the discretization errors of linear solvers. This paper introduces SlerpFlow, a straightforward yet highly effective zero-shot approach that unlocks the full potential of FLUX for high-fidelity inversion and editing. Unlike existing approaches (e.g., RF-Solver) that rely on complex numerical approximations such as high-order Taylor expansions to correct trajectory errors, we present a geometric view based on the Manifold Hypothesis: the empirically observed trajectory curvature is not a numerical artifact, but rather serves as a necessary "centripetal force" that constrains the flow to remain on the data manifold. Guided by this insight, SlerpFlow integrates Spherical Linear Interpolation (Slerp) to rectify flow velocity directions on the hypersphere, strictly adhering to the intrinsic curvature of the latent space. Crucially, by caching the corrected velocity for subsequent steps, SlerpFlow achieves high-precision inversion while maintaining the computational efficiency of a first-order Euler solver. Extensive experiments on FLUX-based reconstruction and editing tasks demonstrate that SlerpFlow improves reconstruction fidelity and achieves stronger semantic alignment in editing without requiring additional training. Code is available at https://github.com/0answer0/SlerpFlow.

With recent advancements in large-scale pre-trained text-to-image (T2I) models, training-free image editing methods have demonstrated remarkable success. Typically, these methods involve adding noise to a clean image via an inversion process, followed by separate denoising steps for the reconstruction and editing paths during the forward process. However, since the reconstruction path is approximated using noisy latents from mismatched timesteps, existing methods inevitably suffer from accumulated drift, which fundamentally limits reconstruction fidelity. To address this challenge, we systematically analyze the inversion process within the flow transformer and propose DirectEdit, a simple yet effective editing method that eliminates the inherent reconstruction error without introducing additional neural function evaluations (NFEs). Unlike most prior works that attempt to rectify the inversion path, DirectEdit focuses on directly aligning the forward paths, enabling precise reconstruction and reliable feature sharing. Furthermore, we introduce a preservation mechanism based on attention feature injection and multi-branch mask-guided noise blending, which effectively balances fidelity and editability. Extensive experiments across diverse scenarios demonstrate that DirectEdit achieves efficient and accurate image editing, delivering superior performance that outperforms state-of-the-art methods. Code and examples are available at https://desongyang.github.io/Directedit.

Inversion-free flow-based image editing avoids latent inversion, but still requires a target-side state at every editing step. The widely used equal-displacement construction keeps the displacement between the noisy source state and the target-side state unchanged across noise levels. This is inconsistent with noising, under which the displacement between two clean states noised with the same noise level and noise sample should contract as the noise level increases. Thus, it can lead to overly aggressive updates at high noise levels. We introduce RIDGE: Re-Noising with Internal Dynamic Guidance for Image Editing, an inversion-free and training-free method that maintains the edited state as an evolving approximation to the unavailable clean target state. RIDGE re-noises this approximation using the same noise level and noise sample as the clean source state, allowing their noisy displacement to decrease naturally with increasing noise. Since the edited state initially contains limited target semantics, RIDGE further applies internal dynamic guidance during the early high-noise steps. A clean target state prediction guides the provisional edited state through a soft dynamic mask derived internally from the model, focusing guidance on regions that require modification without external segmentation or detection models. Experiments on two benchmarks using two backbones, SD3 Medium and FLUX.1-dev, show that RIDGE offers a favorable aggregate trade-off among source preservation, target alignment, and perceptual quality.