Kuramoto Decision Diffusion Models

Diffusion-based decision making has seen explosive popularity due to the ability in producing rich, multimodal trajectories. However, existing frameworks erase the structure of robotic data, which is critical for action fluidity and non-myopic planning, through stochastic noising, then denoise or recover it only probabilistically. This paper aims to address the problem of incorporating spatio-temporal dependencies into the diffusion processes (i.e., forward and reverse), without sacrificing trajectory quality. Building upon and improving the work of Song et al., we propose KDDM, a physics-inspired diffusion paradigm that explicitly encodes the information through Kuramoto-based synchronization. By two neat tricks to harmonize the intertwined chains of Langevin and Kuramoto dynamics, we prove that KDDM elegantly converges to the desired outcome and theoretically outperforms prior approaches. Furthermore, we extend KDDM to ODE-accelerated and guided sampling, enabling its integration with today’s decision-making ecosystem. Experimentally, our proposals achieve superior performance in general, across an extensive range of tasks, including trajectory augmentation, long-horizon planning, and (real-world) robotic control, compared to various diffusion-based solutions.