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

2026-02-10

AI Summary

This work addresses the issue of error accumulation in flow matching–based image generation caused by velocity field adjustments. To mitigate this without requiring retraining, the authors propose two training-free latent trajectory smoothing strategies: Look-Ahead and Look-Back. The Look-Ahead method employs curvature-gated weighted averaging to leverage future trajectory information for forward optimization, while Look-Back dynamically refines the trajectory by applying exponential moving averages over historical paths. As the first trajectory-based—rather than velocity-field-based—smoothing mechanism within the flow matching framework that operates without additional training, the approach effectively suppresses error propagation. Experimental results demonstrate consistently superior generation quality compared to existing training-free methods across multiple benchmarks, including COCO17, CUB-200, and Flickr30K.

Technology Category

• Computer Vision: Motion & Tracking
• Search and Optimization: Learning to Search
• Natural Language Processing: Generation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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.

Problem

• flow matching
• diffusion models
• trajectory smoothing
• training-free generation
• image generation

Innovation

• trajectory smoothing
• training-free generation
• flow matching
• latent trajectory
• diffusion models