Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distance

Understand

Score-based Generative Models (SGMs) aim to sample from a target distribution by learning score functions using samples perturbed by Gaussian noise.

• Existing convergence bounds for SGMs in the W2-distance rely on stringent assumptions about the data distribution.
• In this work, we present a novel framework for analyzing W2-convergence in SGMs, significantly relaxing traditional assumptions such as log-concavity and score regularity.
• Leveraging the regularization properties of the Ornstein--Uhlenbeck (OU) process, we show that weak log-concavity of the data distribution evolves into log-concavity over time.