Kolmogorov Regression for Robust Diffusion Policies

The paper presents a novel approach to finite-dimensional diffusion policies by introducing a backward Kolmogorov equation that enhances performance in long-horizon tasks. Key innovations include replacing stochastic score matching with a deterministic boundary-value PDE, leading to a precision-weighted Cameron-Martin loss that improves trajectory regularity and introduces a deterministic failure detection mechanism. Validation shows significant performance gains, including a 17% increase in maximum episode reward on the PushT benchmark and a 28.4% reduction in RMSE on a manufacturing line, alongside a 96% reduction in deadlock events, highlighting its practical implications for robust policy deployment in real-world applications.