High-Order Matching for One-Step Shortcut Diffusion Models

2025-02-02

AI Summary

First-order single-step diffusion models, which model only velocity, produce trajectories with poor smoothness and geometric alignment—especially in high-curvature regions. To address this, we propose the first distributional transport framework incorporating higher-order kinematics (acceleration and jerk), explicitly integrating higher-order time derivatives into single-step diffusion modeling to theoretically guarantee superior approximation accuracy. Our method synergistically combines higher-order dynamics matching, manifold-aware distribution transport, and convergence analysis, thereby enhancing trajectory smoothness, generation stability, and fidelity to underlying data manifold geometry. Experiments on high-curvature image generation tasks demonstrate that our approach significantly outperforms existing baselines: generated trajectories are markedly smoother, and distribution alignment is substantially more precise. This work establishes a new benchmark for single-step diffusion modeling.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Planning, Routing, and Scheduling: Planning with Language Models
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

One-step shortcut diffusion models [Frans, Hafner, Levine and Abbeel, ICLR 2025] have shown potential in vision generation, but their reliance on first-order trajectory supervision is fundamentally limited. The Shortcut model's simplistic velocity-only approach fails to capture intrinsic manifold geometry, leading to erratic trajectories, poor geometric alignment, and instability-especially in high-curvature regions. These shortcomings stem from its inability to model mid-horizon dependencies or complex distributional features, leaving it ill-equipped for robust generative modeling. In this work, we introduce HOMO (High-Order Matching for One-Step Shortcut Diffusion), a game-changing framework that leverages high-order supervision to revolutionize distribution transportation. By incorporating acceleration, jerk, and beyond, HOMO not only fixes the flaws of the Shortcut model but also achieves unprecedented smoothness, stability, and geometric precision. Theoretically, we prove that HOMO's high-order supervision ensures superior approximation accuracy, outperforming first-order methods. Empirically, HOMO dominates in complex settings, particularly in high-curvature regions where the Shortcut model struggles. Our experiments show that HOMO delivers smoother trajectories and better distributional alignment, setting a new standard for one-step generative models.

Problem

• First-order fast diffusion model
• Image generation
• Complex factor neglect

Innovation

• HOMO Model
• Graph Generation
• Improved Trajectory Smoothness