Reducing Diffusion Model Memorization with Higher Order Langevin Dynamics

TL;DR

This paper investigates how Higher-Order Langevin Dynamics (HOLD) can reduce memorization in diffusion models by regularizing trajectories and imposing dynamical constraints, supported by theoretical analysis and empirical results.

Contribution

It provides the first theoretical analysis of HOLD's regularization effect, showing how increasing model order enhances smoothness and reduces memorization in diffusion models.

Findings

HOLD introduces auxiliary variables that act as velocity and acceleration.

Higher order HOLD results in smoother data trajectories.

Empirical results support the theory that HOLD mitigates memorization.

Abstract

Diffusion/score-based models have emerged as powerful generative models, capable of generating high-quality samples that mimic the training data distribution. However, it has been observed that they are prone to reproducing training samples-known as "memorization"-potentially violating copyright and privacy. In this paper, we study the effect of Higher-Order Langevin Dynamics (HOLD) on this phenomenon. HOLD diffusion processes introduce auxiliary variables; if the data variable is interpreted as "position," then the auxiliary variables can be interpreted as "velocity" and "acceleration," depending on the chosen order of the model. They were originally proposed based on the intuition that they regularize the trajectories of the data variable by implicitly imposing additional dynamical constraints. Our work provides, to our knowledge, the first theoretical characterization of the regularization effect of HOLD. Specifically, we show that in HOLD, the dynamics of the data variable are governed by a low-pass-filtered version of the learned score function, with smoothness increasing with the order of HOLD. We then analyze the optimal empirical score and the possibility of distribution collapse. Together, our results explain the mitigation of memorization as the model order increases. Finally, we present an empirical study on real-world data that supports our theory and highlights this distinct advantage of HOLD over standard diffusion in practice.