Mitigating the Contractivity Trap in Diffusion ODEs via Stein Stabilization

Abstract

A fundamental tension exists in the large-step inference of diffusion models via their deterministic probability flow ordinary differential equation (PF-ODE) paths, which we formally identify as the *contractivity trap*: efficient inference favors large step sizes, while stable convergence requires strong contractivity that limits expressiveness. To address this, we propose SteinDiff, an inference-time stabilization framework based on reference-free Stein corrections. Specifically, SteinDiff introduces a geometry-aware correction mechanism that stabilizes PF-ODE inference trajectories. To this end, we contribute closed-form correction estimators via Stein's identity in the continuous-time setting, enabling the method to adapt to local data geometry. We theoretically demonstrate that SteinDiff reduces integration error even when contractivity is violated and establishes its robustness against discretization-induced distributional shifts. Our analysis further reveals that these corrections act as persistent geometric anchors, providing new insights into the stability of SOTA EDM parameterizations. Extensive experiments demonstrate that SteinDiff significantly mitigates mode collapse and improves generative quality in large-step inference.