Geometry-Aware Discretization Error of Diffusion Models

תקציר מקורי באנגליתarXiv:2605.08392v2 Announce Type: replace Abstract: Practical diffusion sampling requires simulating a reverse-time ODE or SDE with a limited number of denoising steps, making the choice of sampling parameters crucial for minimizing discretization error. Non-asymptotic convergence bounds characterize sampling complexity, but their worst-case constants can obscure target geometry and thereby limit guidance on parameter optimization. Rather than bounding the error, we derive asymptotically exact small-stepsize expansions of Euler-Maruyama weak and Frechet errors for general smooth reverse diffusions, with explicit formulas for Gaussian data. These formulas provide tractable objectives for optimizing diffusion parameters, including the noise and rescaling schedules and the stochasticity coeff