Title: AMC-Solver: Adaptive Multi-Step Cascade with Midpoint Prediction for Efficient Rectified Flow Sampling
Primary area: generative models
Keywords: Adaptive multi-step; Cascaded midpoint prediction; Adams-Bashforth correction; Rectified Flow; Efficient image inversion

Abstract: We propose an Adaptive Multi-step Cascaded solver AMC-Solver, for rectified flow models that integrates a cascaded midpoint predictor with a dynamic-order Adams–Bashforth corrector. At each step, AMC-Solver estimates local error and selects the highest stable order (up to 5), invoking a lightweight corrector only when needed. By reusing intermediate velocity evaluations and dynamically adjusting the integration scheme, AMC-Solver reduces neural network calls by 30–35%. Remarkably, it achieves this efficiency while keeping Frechet Inception Distance (FID) within just 2% of full-precision baselines. The method achieves up to third-order global accuracy when correction is applied. Extensive experiments on image generation and editing tasks show that AMC-Solver outperforms stateof-the-art solvers (FireFlow, RF-Solver, ABM-Solver) in sample quality, inversion fidelity, and efficiency.

TL;DR: We propose AMC-Solver, an adaptive multi-step cascade with midpoint prediction that accelerates rectified flow sampling while preserving image quality.