Efficient Sampling for Score-Based Generative Models via Ninomiya–Victoir Splitting

We propose NV-RK3, an efficient sampler for score-based generative models that applies the Ninomiya–Victoir (NV) splitting scheme [Ninomiya and Victoir, 2008] to the reverse-time stochastic differential equation (SDE). The NV scheme achieves second-order weak convergence by symmetrically decomposing the drift and diffusion flows, in contrast to the first-order Euler–Maruyama (EM) method commonly used in existing score-based samplers. For score SDEs with additive noise, the NV scheme reduces to a fixed-order Strang splitting because the diffusion vector fields are constant in the state, and the drift ODE is integrated with a third- order Runge–Kutta (RK3) method. On CIFAR-10 with the pretrained DDPM++ (continuous) VPSDE model of Song et al. [2021b] and a 50,000-sample FID protocol, NV-RK3 outperforms EM throughout NFE 48–210 under each sampler’s reference terminal handling, with a peak gap of−10.72 FID at NFE 72 (NV-RK3 29.97 vs. EM 40.69); outside this band EM is ahead, by ≈2 FID at NFE ≥600. The two samplers, as implemented in the reference code, differ in their terminal denoising step. Under a shared Tweedie terminal step, NV-RK3 leads at every budget tested (NFE 30–210), by up to−43.4 FID at NFE 60, so the ordering of the two integrators is not an artifact of the baseline’s terminal handling, even though the absolute FID values are sensitive to it. Extension to Sub-VPSDE/VESDE and a quasi-Monte Carlo ablation are left to future work.