CAB: Accelerating Flow and Diffusion Sampling via Rectification and Corrected Adams-Bashforth

Flow and diffusion models achieve high-fidelity, high-resolution image synthesis, but often require many function evaluations (NFEs) at sampling time. Existing acceleration methods either require additional training through distillation or rely on training-free high-order solvers, and both can degrade sample quality at low NFE budgets. We propose CAB (Corrected Adams-Bashforth), a training-free sampler that accelerates both flow and diffusion models. CAB first transforms the sampling dynamics to a common rectified coordinate system, and then applies a multistep Adams--Bashforth predictor augmented with a simple correction term based on past velocity evaluations and therefore incurs no additional NFEs. The resulting method is simple, has the same algorithmic form across model classes, and has at least third-order local truncation error and second-order global error. Experiments on pretrained flow and diffusion models, including class-conditional and large-scale text-to-image benchmarks, show that CAB improves quality--NFE trade-offs in the low-step regime of (6)--(20) NFEs. It also remains competitive with strong training-free samplers at higher step counts across most tested models.