Kolmogorov Regression for Robust Diffusion Policies
A backward Kolmogorov equation lifts diffusion policies to a Cameron-Martin space, replacing stochastic score matching with a deterministic PDE. This approach achieves convergence bounds tied to kernel effective rank, improved trajectory regularity, and a failure detector without rewards, showing 17% higher reward and 67.6% reduced drift on PushT, and 28.4% lower RMSE with perfect bottleneck detection on a manufacturing line. Hamilton-Jacobi theory reduces deadlock events by 96% in simulations.