A Favorable Regime Between ODE and SDE for Few-Step Diffusion Sampling

Few-step diffusion sampling sharpens the tension between ODE and SDE dynamics. ODE samplers are stable but can lose diversity, while the standard SDE endpoint can become unreliable at low numbers of function evaluations (NFE). The challenge is therefore not simply whether stochasticity should be added, but which driver properties allow stochastic correction to contribute diffusion without losing finite-step control. We show that this tradeoff is governed by two driver-level quantities, the asymptotic covariance $Q$, which sets the effective diffusion level on the ODE-to-SDE spectrum, and the Poisson solution norm $C_\chi$, which controls the finite-step remainder. Gaussian drivers have $C_\chi = \infty$, so this finite-step remainder is not uniformly controlled by the same bound. Balancing the diffusion level set by $Q$ with the finite-step control set by $C_\chi$ formalizes a favorable regime for bounded structured drivers with intermediate diffusion strength. This regime directly gives a structured correction method, instantiated as Fast-Driver Sampler (FDS) with the shuffled-Lorenz driver. Across DiT-XL/2 and EDM2, FDS establishes a stronger low-NFE frontier among evaluated training-free samplers, improving ODE baselines while avoiding the degradation of the SDE endpoint.