ParaFlow: Parallel Sampling for Flow Matching Models

This paper addresses the fundamental challenge of accelerating the inherently autoregressive sampling process in Flow Matching (FM) models through a numerical systems perspective. We introduce ParaFlow, a training-free framework that recasts sampling as a system of Triangular Nonlinear Equations (TNEs) to enable step-level parallelism. Unlike existing parallel samplers for diffusion models that require 2–3× more function evaluations (NFEs), we propose a velocity approximation scheme that leverages the temporal smoothness of FM trajectories. This allows ParaFlow to perform parallel sampling on a single GPU while requiring less total NFE count to the standard sequential sampler. We theoretically guarantee that our method converges to the exact autoregressive trajectory and that our approximation maintains negligible error bounds. Extensive experiments on Stable Diffusion 3 and Flux demonstrate that ParaFlow achieves up to 4.3× wall-clock speedup with negligible impact on quality, making high-performance parallel sampling truly practical for resource-constrained settings. The source code is released in the supplementary materials. Code is available at https://github.com/Jianrong-Lu/ParaFlow.