Diverse Sampling in Diffusion Models with Divergence-Free Particle Guidance

Modern generative models can produce high-quality samples, but independent samples under the same condition often yields highly similar outputs. Particle-based methods increase diversity by letting the samples in a batch interact, typically through a repulsive force. These forces, however, also push each sample away from the data distribution and produce visible artifacts. We introduce EDDY, a training-free particle guidance method designed to avoid this failure mode. Instead of a repulsive gradient, EDDY couples particles through anti-symmetric matrix fields passed through a Stein operator, a family of drift perturbations that leaves the Fokker–Planck equation invariant. Unlike repulsive guidance, these interactions do not alter a particle's distribution while the batch is independent. For the same reason they cannot create diversity on their own, so EDDY pairs them with a negatively correlated initialization that keeps each particle's prior exact. To use EDDY with perceptual kernels such as DINOv2, we approximate its second-order terms with finite differences and Hutchinson estimates. Across FLUX.1-dev, FLUX.2-klein and SDXL, EDDY achieves higher image quality and prompt alignment than existing particle guidance methods at matched diversity.