Why Diffusion Models Outperform Langevin Dynamics

In recent research, the limitations of Langevin dynamics in handling high-dimensional distributions have been starkly highlighted. This study critically examines score-based generative models, specifically contrasting Langevin dynamics with diffusion models. It reveals significant vulnerabilities in Langevin dynamics when faced with even minuscule errors in score function estimates.

Score Function Estimation Errors

Langevin dynamics have long been a tool of choice for sampling in generative models. However, this research points to a critical flaw: their lack of robustness to L²errors (and more generally L^perrors) in estimating the score function. In practical terms, this means that even with tiny inaccuracies, the output distribution diverges significantly from the target distribution when measured in Total Variation (TV) distance.

Diffusion Models Hold Their Ground

Diffusion models, on the other hand, show remarkable resilience under similar conditions. The specification is as follows: they can sample accurately from target distributions within polynomial time, even when faced with slight errors in score function estimation. This robustness underlines the foundational stability of diffusion models, particularly relevant in applications requiring precision and reliability.

Practical Implications

Why does this matter? In real-world applications, perfect score function estimation is unattainable due to data limitations. This makes the choice of model critical. Developers should note the breaking change in reliability when opting for Langevin dynamics, especially in high-dimensional contexts. Should practitioners continue to rely on a method that falters under inevitable estimation errors?

The findings signal a clear preference for diffusion models in scenarios where the integrity of the output distribution is critical. With the potential for significant deviations in Langevin dynamics, the risk may not justify their use, especially when diffusion models offer a more stable alternative.

, while Langevin dynamics have their place in generative modeling, the choice must be data-driven and context-specific. As this study underscores, the stakes in high-dimensional spaces are high, and choosing the wrong tool could lead to misleading results.