We present a novel method for simulating infinite-dimensional conditional stochastic processes governing surface shape evolution. Given boundary conditions represented as spherical functions, we consider a function-valued diffusion process X with initial state \(X_0\) , conditioned on \(X_T\) . To address the simulation challenge, we develop a neural operator architecture leveraging spherical harmonic transforms to approximate the intractable drift term arising from Doob’s h-transform. The proposed operator demonstrates discretization equivariance, enabling direct application to spherical meshes at arbitrary resolutions without architectural modifications or retraining. We validate our method on several synthetic shape evoluation scenarios.