Lekan Molu
To address temporal drift in diffusion policies, this work introduces a backward Kolmogorov equation to replace stochastic score matching with a deterministic PDE, proposing a Cameron-Martin loss and a residual diagnostic.
Finite-dimensional diffusion policies suffer from temporal drift due to discretization artifacts when deployed on physical systems, degrading long-horizon performance.
Lift diffusion policies to a Cameron-Martin space using the backward Kolmogorov equation, replacing stochastic score matching with a deterministic boundary-value PDE. Leverage Gaussian measure theory to realize the noise covariance operator from a colored noise distribution. Train with a precision-weighted Cameron-Martin loss and introduce a Kolmogorov residual as a PDE diagnostic during inference.
On PushT manipulation benchmark: 17% improvement in max episode reward (0.95 vs 0.78), 67.6% reduction in inter-step drifts. On CONWIP manufacturing line: 28.4% lower RMSE than LSTM, perfect starvation recall (1.0), bottleneck Precision@1=1.0. Hamilton-Jacobi reachability reduces deadlock events by 96%.