SlerpFlow: Spherical Trajectory Correction for Rectified Flow Inversion

Rectified flow models, such as FLUX, rely on the ability to invert images back to latent noise for high-fidelity reconstruction and editing. However, standard numerical solvers (like Euler or Taylor-based methods) suffer from discretization errors that accumulate over time, leading to poor reconstruction quality. This paper investigates whether the observed trajectory curvature in these models is merely a numerical artifact or a geometric necessity, and proposes a new solver, SlerpFlow, to address this.

The authors propose a geometric interpretation based on the Manifold Hypothesis: the curvature observed in learned trajectories acts as a centripetal force that keeps the flow within the high-density region of the data manifold. Standard Euclidean solvers fail because they move tangentially, causing the trajectory to drift away from this manifold. SlerpFlow addresses this by decoupling the latent dynamics into radial and angular components. It uses Spherical Linear Interpolation (Slerp) to predict the next direction on the hypersphere, ensuring the update adheres to the intrinsic curvature of the latent space. By caching this corrected velocity, the method achieves high-precision inversion without increasing the number of function evaluations (NFE) compared to standard first-order solvers.

Experimental results on FLUX-based models demonstrate that SlerpFlow significantly outperforms existing solvers like RF-Solver and FireFlow in both reconstruction fidelity and semantic editing tasks. By strictly adhering to the radial dynamics and minimizing angular discretization error, SlerpFlow maintains structural consistency during the inversion process. The authors show that this geometric approach provides a more stable trajectory, leading to better alignment between the source image and the edited output without requiring additional training or extra computational overhead.