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原文摘要

Diffusion transformer models deliver state-of-the-art image synthesis quality but suffer from prohibitively slow iterative sampling. Although reducing sampling steps accelerates inference, aggressive step schedules often distort intermediate features and degrade sample fidelity. We present GeoRK2, a training-free framework that bridges numerical analysis and information geometry. GeoRK2 couples a second-order Runge-Kutta (RK2) integrator with a curvature-aware geometric flow derived from the model's noise predictions, promoting stable feature evolution under manifold-aware integration. By leveraging an empirical feature covariance-induced metric estimated from activation covariances to capture intrinsic feature geometry, GeoRK2 constrains error propagation under large-step integration while preserving structural fidelity. As a fully plug-and-play method, GeoRK2 requires no retraining and is compatible with mainstream pre-trained diffusion transformers. Comprehensive experiments on image generation and text-to-video generation tasks across representative diffusion backbones (e.g., DiT-XL, HunyuanVideo, and FLUX.1-dev) demonstrate that GeoRK2 achieves 4-5x faster inference than baseline frameworks with only marginal perceptual differences (DFID 0.81), confirming its effectiveness and generality.