ParaPC-FM: Accelerating Parallel Sampling via Principled Initialization

Flow matching and diffusion models achieve high-quality generation by solving continuous-time generative dynamics, but their sampling remains inherently sequential and costly. Parallel sampling reduces wall-clock latency, yet often requires many function evaluations (NFEs) due to inaccurate future-state initialization and repeated correction. We propose ParaPC-FM, a fixed-point predictor--corrector framework that unifies high-order solver correction and future-state initialization, enabling both components to be incorporated into different parallel samplers. In particular, our UniP-based truncated initialization reuses past velocity predictions to estimate future states more accurately, reducing correction iterations and NFEs with almost no additional overhead. On a ParaDiGMS-style framework, ParaPC-FM achieves up to $1.25\times$ and $1.49\times$ speedups on FLUX.1-dev at $50$ and $100$ steps, and up to $1.22\times$ and $1.16\times$ speedups on Stable Diffusion 3 and Stable Diffusion 3.5 at $50$ steps. When integrated into ParaTAA, the proposed initialization further achieves up to $1.17\times$ speedup at $50$ steps. Importantly, these acceleration gains are obtained while keeping image quality nearly unchanged.