Recent advances have reformulated diffusion models as deterministic ordinary differential equations (ODEs) through the framework of flow matching, providing a unified formulation for the noise-to-data generative process. Various training-free flow matching approaches have been developed to improve image generation through flow velocity field adjustment, eliminating the need for costly retraining. However, Modifying the velocity field $v$ introduces errors that propagate through the full generation path, whereas adjustments to the latent trajectory $z$ are naturally corrected by the pretrained velocity network, reducing error accumulation. In this paper, we propose two complementary training-free latent-trajectory adjustment approaches based on future and past velocity $v$ and latent trajectory $z$ information that refine the generative path directly in latent space. We propose two training-free trajectory smoothing schemes: \emph{Look-Ahead}, which averages the current and next-step latents using a curvature-gated weight, and \emph{Look-Back}, which smoothes latents using an exponential moving average with decay. We demonstrate through extensive experiments and comprehensive evaluation metrics that the proposed training-free trajectory smoothing models substantially outperform various state-of-the-art models across multiple datasets including COCO17, CUB-200, and Flickr30K.

翻译：近期研究进展通过流匹配框架将扩散模型重新表述为确定性常微分方程（ODE），为噪声到数据的生成过程提供了统一形式化。多种无训练的流匹配方法通过调整流速场以改进图像生成，从而避免了昂贵的重新训练。然而，修改速度场$v$会引入沿整个生成路径传播的误差，而对潜在轨迹$z$的调整可由预训练速度网络自然校正，从而减少误差累积。本文提出两种互补的无训练潜在轨迹调整方法，基于未来与历史的速度$v$及潜在轨迹$z$信息，直接在潜在空间中优化生成路径。我们设计了两种无训练轨迹平滑方案：\emph{前瞻法}——使用曲率门控权重对当前与下一步潜在变量进行加权平均；\emph{回溯法}——采用指数移动平均衰减机制平滑潜在变量。通过大量实验与综合评估指标，我们证明所提出的无训练轨迹平滑模型在COCO17、CUB-200和Flickr30K等多个数据集上显著优于各类前沿模型。