Popular diffusion-based sampling methods have a fundamental limitation for multimodal distributions—they require exponentially long times to transition between well-separated modes, making theoretical convergence guarantees misleading about practical efficiency.
This paper challenges the claim that Wasserstein gradient flows and forward-only diffusion can efficiently sample complex multimodal distributions. Using tools from statistical physics, the authors prove these methods suffer from exponentially slow mixing times when modes are well-separated, regardless of theoretical convergence guarantees.