Stein Guidance without Gradients: Discretization Uniform Diffusion Inference Time Scaling beyond Particle SMC

Diffusion inference can scale through more solver steps or larger trajectory ensembles. These define the numerical depth $n$ and statistical width $N$. In Sequential Monte Carlo (SMC) with full resampling at every solver step, the resampling depth also equals $n$. A scalable method should decouple depth and width: the number of trajectories needed for a prescribed sampling accuracy should remain bounded as numerical depth increases. Repeated resampling can violate this principle: we construct a Brownian example with single-output total variation (TV) error $\Theta (n/N)$ for $2\le n\le N$. This raises a central question: how can we decouple sequential and statistical complexity, so that increasing $n$ does not force $N$ to grow merely to maintain accuracy? We propose \method, a family of derivative-free guidance methods based on Gaussian Stein's identity, with whole-path independence Metropolis–Hastings (MH) correction. Each proposal uses value-weighted candidate selection along one trajectory. The value function need not be exact. Approximate values steer trajectories toward promising regions, while a derivative free MH correction applied after generation can asymptotically remove the bias introduced by the approximation. Generating proposal paths independently avoids the shared ancestry caused by resampling across particles. Under uniform value and spatial bounds, our theory guarantees that the number of complete proposals needed for a prescribed finite-grid sampling accuracy stays bounded or even decreases as numerical depth increases. Stein guidance also parallelizes value queries within each trajectory. At a fixed per-proposal query budget, the pool-noise term in the error bound has the same order for every pool size $K\ge 2$.