Finite-Particle Convergence Bounds for Conservative Drifting Generative Models

A new technique for conservative drifting in one-step generative modeling has been developed. Instead of relying on the usual displacement-based drifting velocity, this method uses a velocity derived from the KDE-gradient, which is determined by comparing smoothed data with model scores. This approach effectively tackles the issues of non-conservatism found in standard displacement fields. The study sets forth convergence bounds for continuous-time finite particles in ℝᵈ, utilizing a joint-entropy identity to manage empirical Stein drift, the smoothed Fisher discrepancy, and the squared center velocity. A significant adjustment for finite-particle dynamics includes a reciprocal-KDE self-interaction term, adhering to deterministic and high-probability local-occupancy conditions. This technique works for both conservative and non-conservative drifting models, bolstering the foundations of generative modeling.