Look-Ahead and Look-Back Flows: Training-Free Image Generation with Trajectory Smoothing

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.